a=8,b=12,c=17a=8,b=12,c=17 Use Heron’s Area Formula to find the area of the triangle

# a=8,b=12,c=17a=8,b=12,c=17 Use Heron’s Area Formula to find the area of the triangle

• MATH

u=<7,1>,v=<−3,2>u=<7,1>,v=<-3,2> Find u⋅vu⋅v.

You need to evaluate the product of the vectors u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅ju=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j , such that: u⋅v=ux⋅vx+uy⋅vyu⋅v=ux⋅vx+uy⋅vy u⋅v=(7)⋅(−3)+1⋅(2)u⋅v=(7)⋅(-3)+1⋅(2) u⋅v=−21+2u⋅v=-21+2 u⋅v=−19u⋅v=-19 Hence, evaluating…

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v=i+2j,w=2i−jv=i+2j,w=2i-j Use the Law of Cosines to find the angle αα…

You need to use the dot product to find the cosine of the angle between the vectors v and w, such that: cosα=v⋅w|v|⋅|w|cosα=v⋅w|v|⋅|w| You need to evaluate the product of the vectors v and w,

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v=i+j,w=2i−2jv=i+j,w=2i-2j Use the Law of Cosines to find the angle αα…

You need to use the dot product to find the cosine of the angle between the vectors v and w, such that: cosα=v⋅w|v|⋅|w|cosα=v⋅w|v|⋅|w| You need to evaluate the product of the vectors v and w,

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||v||=43–√,θ=0∘||v||=43,θ=0∘ Find the component form of vv given its magnitude and the…

The magnitude of a vector u=a⋅i+b⋅ju=a⋅i+b⋅j , such that: |u|=a2+b2−−−−−−√|u|=a2+b2 Since the problem provides the magnitude |v|=43–√|v|=43 , yields: 43–√=a2+b2−−−−−−√43=a2+b2 The direction angle of the…

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||v||=23–√,θ=45∘||v||=23,θ=45∘ Find the component form of vv given its magnitude and…

You need to find the component form of the vector v=<a,b>v=<a,b> , hence, you need to use the information provided. You need to evaluate the magnitude |v|, such that: |v|=a2+b2−−−−−−√|v|=a2+b2…

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||v||=34,θ=150∘||v||=34,θ=150∘ Find the component form of vv given its magnitude and the…

You need to find the component form of the vector v = <a,b>, hence, you need to use the information provided. You need to evaluate the magnitude |v|, such that: |v|=a2+b2−−−−−−√|v|=a2+b2

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||v||=72,θ=150∘||v||=72,θ=150∘ Find the component form of vv given its magnitude and the…

The magnitude of a vector u=a⋅i+b⋅ju=a⋅i+b⋅j , such that: |u|=a2+b2−−−−−−√|u|=a2+b2 Since the problem provides the magnitude |v|=72|v|=72 , yields: 72=a2+b2−−−−−−√72=a2+b2 The direction angle of the vector…

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||v||=1,θ=45∘||v||=1,θ=45∘ Find the component form of vv given its magnitude and the…

The magnitude of a vector u=a⋅i+b⋅ju=a⋅i+b⋅j , such that: |u|=a2+b2−−−−−−√|u|=a2+b2 Since the problem provides the magnitude |v|=1|v|=1 , yields: 1=a2+b2−−−−−−√1=a2+b2 The direction angle of the vector can…

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||v||=3,θ=0∘||v||=3,θ=0∘ Find the component form of vv given its magnitude and the…

The magnitude of a vector u=a⋅i+b⋅j,u=a⋅i+b⋅j, such that: |u|=a2+b2−−−−−−√|u|=a2+b2 Since the problem provides the magnitude |v|=3|v|=3 , yields: 3=a2+b2−−−−−−√3=a2+b2 The direction angle of the vector can be…

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v=8(cos(135∘)i+sin(135∘)j)v=8(cos(135∘)i+sin(135∘)j) Find the magnitude and direction angle of the…

The magnitude of a vector v=vx⋅i+vy⋅jv=vx⋅i+vy⋅j is given by the following formula, such that: |v|=v2x+v2y−−−−−−√|v|=vx2+vy2 |v|=8cos2135o+8sin2135o−−−−−−−−−−−−−−−−−−−√|v|=8cos2135o+8sin2135o

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v=3(cos(60∘)i+sin(60∘)j)v=3(cos(60∘)i+sin(60∘)j) Find the magnitude and direction angle of the…

The magnitude of a vector v=vx⋅i+vy⋅jv=vx⋅i+vy⋅j is given by the following formula, such that: |v|=v2x+v2y−−−−−−√|v|=vx2+vy2 |v|=9cos260o+9sin260o−−−−−−−−−−−−−−−−−√|v|=9cos260o+9sin260o|v|=9(cos260o+sin260o)−−−−−−−−−−−−−−−−−√|v|=9(cos260o+sin260o)…

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v=−5i+4jv=-5i+4j Find the magnitude and direction angle of the vector vv.

The magnitude of a vector u=a⋅i+b⋅ju=a⋅i+b⋅j , such that: |u|=a2+b2−−−−−−√|u|=a2+b2 In the problem, the vector v=−5i+4j,v=-5i+4j, hence, its’ magnitude is:

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v=6i−6jv=6i-6j Find the magnitude and direction angle of the vector vv.

If the system (i,j)(i,j) is orthonormal then the magnitude of vv is 62+(−6)2−−−−−−−−−−√=62–√.62+(-6)2=62. Also, the tangent of a direction angle is −66=−1,-66=-1, and the angle itself is 7π47π4 (the fourth…

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||v||=8,u=⟨3,3⟩||v||=8,u=〈3,3〉 Find the vector vv with the given magnitude and…

The magnitude of a vectoru=a⋅i+b⋅j,u=a⋅i+b⋅j, such that: |u|=a2+b2−−−−−−√|u|=a2+b2 Since the problem provides the magnitude |v|=8|v|=8 , yields: 8=a2+b2−−−−−−√8=a2+b2 The direction angle of the vector can be…

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||v||=5,u=⟨2,5⟩||v||=5,u=〈2,5〉 Find the vector vv with the given magnitude and…

The magnitude of a vector u=a⋅i+b⋅ju=a⋅i+b⋅j , such that: |u|=a2+b2−−−−−−√|u|=a2+b2 Since the problem provides the magnitude |v|=5|v|=5 , yields: 5=a2+b2−−−−−−√5=a2+b2 The direction angle of the vector can…

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||v||=3,u=⟨−12,−5⟩||v||=3,u=〈-12,-5〉 Find the vector vv with the given magnitude…

You need to find the component form of the vector v=<a,b>v=<a,b> , hence, you need to use the information provided. You need to evaluate the magnitude |v|, such that: |v|=a2+b2−−−−−−√|v|=a2+b2

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||v||=10,u=⟨−3,4⟩||v||=10,u=〈-3,4〉 Find the vector vv with the given magnitude…

The magnitude of a vector v=vx⋅i+vy⋅jv=vx⋅i+vy⋅j is given by the following formula, such that: |v|=v2x+v2y−−−−−−√|v|=vx2+vy2 The problem provides the information that |v| = 10: 10=v2x+v2y−−−−−−√10=vx2+vy2 You…

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w=7j−3iw=7j-3i Find a unit vector in the direction of the given vector. Verify that the…

For a nonzero vector ww a unit vector aa with the same direction may be found by the formula a=(1||w||)⋅w.a=(1||w||)⋅w. It has the same direction because it is a ww multiplied by a positive number. It has…

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w=i−2jw=i-2j Find a unit vector in the direction of the given vector. Verify that the…

For a nonzero vector ww a unit vector aa with the same direction may be found by the formula a=(1||w||)⋅w.a=(1||w||)⋅w. It has the same direction because it is a ww multiplied by a positive number. It has…

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w=−6iw=-6i Find a unit vector in the direction of the given vector. Verify that the…

For a nonzero vector ww a unit vector aa with the same direction may be found by the formula a=(1||w||)⋅w.a=(1||w||)⋅w. It has the same direction because it is a ww multiplied by a positive number. It has…

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w=4jw=4j Find a unit vector in the direction of the given vector. Verify that the result…

Hence, you need to find the unit vector having the same direction as the vector w=4j⇒w=<0,4>w=4j⇒w=<0,4> , hence, you need to use the formula, such that: u=w|w|u=w|w| You need to evaluate the…

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v=6i−2jv=6i-2j Find a unit vector in the direction of the given vector. Verify that the…

For a nonzero vector ww a unit vector aa with the same direction may be found by the formula a=(1||w||)⋅w.a=(1||w||)⋅w. It has the same direction because it is a ww multiplied by a positive number. It…

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v=i+jv=i+j Find a unit vector in the direction of the given vector. Verify that the…

For a nonzero vector ww a unit vector aa with the same direction may be found by the formula a=(1||w||)⋅w.a=(1||w||)⋅w. It has the same direction because it is a ww multiplied by a positive number. It has…

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v=⟨5,−12⟩v=〈5,-12〉 Find a unit vector in the direction of the given vector….

Hence, you need to find the unit vector having the same direction as the vector v=<5,−12>v=<5,-12> , hence, you need to use the formula, such that: u=v|v|u=v|v| You need to evaluate the magnitude…

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v=⟨−2,2⟩v=〈-2,2〉 Find a unit vector in the direction of the given vector. Verify…

Hence, you need to find the unit vector having the same direction as the vector v=<−2,2>v=<-2,2> , hence, you need to use the formula, such that: u=v|v|u=v|v| You need to evaluate the magnitude…

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u=⟨0,−2⟩u=〈0,-2〉 Find a unit vector in the direction of the given vector. Verify…

Hence, you need to find the unit vector having the same direction as the vector v=<0,−2>v=<0,-2> , hence, you need to use the formula, such that: u=v|v|u=v|v| You need to evaluate the magnitude…

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v=⟨3,0⟩v=〈3,0〉 Find a unit vector in the direction of the given vector. Verify that…

Hence, you need to find the unit vector having the same direction as the vector v=<3,0>v=<3,0> , hence, you need to use the formula, such that: u=v|v|u=v|v| You need to evaluate the magnitude…

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u=2j,v=3iu=2j,v=3i Find (a) u+vu+v, (b) u−vu-v

You need to perform the addition of the vectors u and v,u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅ju=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j , such that: u+v=(ux+vx)i+(uy+vy)ju+v=(ux+vx)i+(uy+vy)j u+v=(0+3)i+(2+0)ju+v=(0+3)i+(2+0)j u+v=3i+2ju+v=3i+2j Hence,…

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u=2i,v=ju=2i,v=j Find (a) u+vu+v, (b) u−vu-v, and (c) 2u−3v2u-3v.

You need to evaluate the sum of two vectors,u+v, hence you need to perform the addition of the same versors, such that: u = 2i + 0j v = 0i + j u + v = (2+0)i + (0+1)j u + v = 2i+j Hence,…

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u=−2i+j,v=3ju=-2i+j,v=3j Find (a) u+vu+v, (b) u−vu-v, and (c) 2u−3v2u-3v.

You need to evaluate the sum of two vectors,u+vu+v , hence you need to perform the addition of the same versors, such that: u=−2i+ju=-2i+j v=0i+3jv=0i+3j u+v=(−2+0)i+(1+3)ju+v=(-2+0)i+(1+3)j u+v=−2i+4ju+v=-2i+4j…

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u=i+j,v=2i−3ju=i+j,v=2i-3j Find (a) u+vu+v, (b) u−vu-v, and (c)

You need to evaluate the sum of two vectors,u+v,u+v, hence you need to perform the addition of the same versors, such that: u=i+ju=i+j v=2i−3jv=2i-3j u+v=(1+2)i+(1−3)ju+v=(1+2)i+(1-3)j u+v=3i−2ju+v=3i-2j…

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u=⟨0,0⟩,v=⟨2,1⟩u=〈0,0〉,v=〈2,1〉 Find (a) u+vu+v, (b)

You need to evaluate the sum of two vectors,u+vu+v , hence you need to perform the addition of the same versors, such that: u=<0,0>⇒u=0i+0ju=<0,0>⇒u=0i+0j v=<2,1>⇒v=2i+jv=<2,1>⇒v=2i+j

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u=⟨−5,3⟩,v=⟨0,0⟩u=〈-5,3〉,v=〈0,0〉 Find (a) u+vu+v, (b)

For vectors given in a component form linear combinations are also performed by components. u=<−5,3>,u=<-5,3>, v=<0,0>,v=<0,0>,therefore (a) u+v=<−5+0,3+0>=<−5,3>,u+v=<-5+0,3+0>=<-5,3>, (b)

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u=⟨2,3⟩,v=⟨4,0⟩u=〈2,3〉,v=〈4,0〉 Find (a) u+vu+v, (b)

For vectors in a coordinate form their linear combinations are also performed by coordinates. u=<2,3>,v=<4,0>,u=<2,3>,v=<4,0>,therefore (a) u+v=<2+4,3+0>=<6,3>,u+v=<2+4,3+0>=<6,3>, (b)

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u=⟨2,1⟩,v=⟨1,3⟩u=〈2,1〉,v=〈1,3〉 Find (a) u+vu+v, (b)

For vectors in a coordinate form their linear combinations are also performed by coordinates. u=<2,1>,u=<2,1>, v=<1,3>,v=<1,3>,therefore (a) u+v=<2+1,1+3>=<3,4>,u+v=<2+1,1+3>=<3,4>, (b)

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a=35,b=58,c=38a=35,b=58,c=38 Use Heron’s Area Formula to find the area of the triangle.

The Heron’s Formula is used to compute the area of the triangle when the three sides are known. The formula is: A=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√A=s(s-a)(s-b)(s-c) where s is the semi-perimeter of the triangle, and a, b…

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a=1,b=12,c=34a=1,b=12,c=34 Use Heron’s Area Formula to find the area of the triangle.

The Heron’s formula is: A=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√A=s(s-a)(s-b)(s-c) where s is the semi-perimeter of triangle, and a, b and c are the length of the sides. The semi-perimeter of the given triangle is:…

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a=3.05,b=0.75,c=2.45a=3.05,b=0.75,c=2.45 Use Heron’s Area Formula to find the area of the triangle.

Given a=3.05,b=0.75,c=2.45a=3.05,b=0.75,c=2.45 Heron’s Area Formula A=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√A=s(s-a)(s-b)(s-c) where s=a+b+c2s=a+b+c2 s=3.05+0.75+2.452=6.252=3.125s=3.05+0.75+2.452=6.252=3.125 A=(3.125)(3.125−3.05)(3.125−0.75)(3.125−2.45)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√A=(3.125)(3.125-3.05)(3.125-0.75)(3.125-2.45)…

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a=12.32,b=8.46,c=15.05a=12.32,b=8.46,c=15.05 Use Heron’s Area Formula to find the area of the triangle.

When the three sides of the triangle are known, its area can be solved using the Heron’s formula. A=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√A=s(s-a)(s-b)(s-c) where a, b and c are the length of the three sides and s is half of…

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a=75.4,b=52,c=52a=75.4,b=52,c=52 Use Heron’s Area Formula to find the area of the triangle.

Given: a=75.4,b=52,b=52a=75.4,b=52,b=52 Heron’s area formula A=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√A=s(s-a)(s-b)(s-c) where s=a+b+c2s=a+b+c2 s=75.4+52+522=179.42=89.7s=75.4+52+522=179.42=89.7 A=(89.7)(89.7−75.4)(89.7−52)(89.7−2)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√A=(89.7)(89.7-75.4)(89.7-52)(89.7-2)…

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a=2.5,b=10.2,c=9a=2.5,b=10.2,c=9 Use Heron’s Area Formula to find the area of the triangle.

Given: a=2.5,b=10.2,c=9a=2.5,b=10.2,c=9 Heron’s Area Formula A=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√A=s(s-a)(s-b)(s-c) where s=a+b+c2s=a+b+c2 s=2.5+10.2+92=21.72=10.85s=2.5+10.2+92=21.72=10.85 A=10.85(10.85−2.5)(10.85−10.2)(10.85−9)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√A=10.85(10.85-2.5)(10.85-10.2)(10.85-9) …

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a=33,b=36,c=25a=33,b=36,c=25 Use Heron’s Area Formula to find the area of the triangle.

Given: a=33,b=36,c=25a=33,b=36,c=25 Heron’s Area formula is A=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√A=s(s-a)(s-b)(s-c) where s=a+b+c2s=a+b+c2 s=33+36+252=942=47s=33+36+252=942=47 A=47(47−33)(47−36)(47−25)−−−−−−−−−−−−−−−−−−−−−−−−√A=47(47-33)(47-36)(47-25) A=47(14)(11)(22)−−−−−−−−−−−−√A=47(14)(11)(22)…

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a=8,b=12,c=17a=8,b=12,c=17 Use Heron’s Area Formula to find the area of the triangle.

Given: a=8,b=12,c=17a=8,b=12,c=17 Heron’s Area Formula A=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√A=s(s-a)(s-b)(s-c) where s=a+b+c2s=a+b+c2 s=8+12+172=372=18.5s=8+12+172=372=18.5 A=18.5(18.5−8)(18.5−12)(18.5−17)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√A=18.5(18.5-8)(18.5-12)(18.5-17) A=18.5(10.5)(6.5)(1.5)−−−−−−−−−−−−−−−√A=18.5(10.5)(6.5)(1.5)…

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a=160,B=12∘,C=7∘a=160,B=12∘,C=7∘ Determine whether the Law of Sines or the Law of Cosines is…

Given: a=160,B=12∘,C=7∘a=160,B=12∘,C=7∘ Law of Sines asin(A)=bsin(B)=csin(C)asin(A)=bsin(B)=csin(C) A=180−12−17A=180-12-17 A=161∘A=161∘ 160sin(161)=bsin(12)=csin(7)160sin(161)=bsin(12)=csin(7) 160sin(161)=bsin(12)160sin(161)=bsin(12) b=160sin(12)sin(161)b=160sin(12)sin(161)…

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A=42∘,B=35∘,c=1.2A=42∘,B=35∘,c=1.2 Determine whether the Law of Sines or the Law of Cosines is…

Given A=42,B=35,c=1.2A=42,B=35,c=1.2 Law of Sines asin(A)=bsin(B)=csin(C)asin(A)=bsin(B)=csin(C) C=180−42−35C=180-42-35 C=103C=103 asin(42)=bsin(35)=1.2sin(103)asin(42)=bsin(35)=1.2sin(103) asin(42)=1.2sin(103)asin(42)=1.2sin(103) a=1.2sin(42)sin(103)a=1.2sin(42)sin(103) a=.82a=.82…

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a=11,b=13,c=7a=11,b=13,c=7 Determine whether the Law of Sines or the Law of Cosines is needed…

Given a=11,b=13,c=7a=11,b=13,c=7 cos(B)=a2+c2−b22accos(B)=a2+c2-b22ac cos(B)=112+72−1322⋅11⋅7cos(B)=112+72-1322⋅11⋅7 cos(B)=.0065cos(B)=.0065   B=arccos(.0065)B=arccos(.0065) B=89.63∘B=89.63∘ cos(A)=b2+c2−a22bccos(A)=b2+c2-a22bc …

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A=24∘,a=4,b=18A=24∘,a=4,b=18 Determine whether the Law of Sines or the Law of Cosines is needed…

Given: A=24∘,a=4,b=18A=24∘,a=4,b=18 Law of Sines asin(A)=bsin(B)=csin(C)asin(A)=bsin(B)=csin(C) 4sin(24)=18sin(B)=csin(C)4sin(24)=18sin(B)=csin(C) 4sin(24)=18sin(B)4sin(24)=18sin(B) sin(B)=18sin(24)4sin(B)=18sin(24)4 sin(B)=1.8303sin(B)=1.8303 B=arcsin(1.8303)B=arcsin(1.8303) Angle B does…

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a=10,b=12,C=70∘a=10,b=12,C=70∘ Determine whether the Law of Sines or the Law of Cosines is…

Given: a=10,b=12,C=70∘a=10,b=12,C=70∘ c2=a2+b2−2abcos(C)c2=a2+b2-2abcos(C) c2=102+122−2⋅10⋅12⋅cos(70)c2=102+122-2⋅10⋅12⋅cos(70) c2=161.915c2=161.915 c=12.72c=12.72 cos(B)=a2+c2−b22accos(B)=a2+c2-b22ac cos(B)=102+12.722−1222⋅10⋅12.72cos(B)=102+12.722-1222⋅10⋅12.72…

• MATH

a=8,c=5,B=40∘a=8,c=5,B=40∘ Determine whether the Law of Sines or the Law of Cosines is needed…

Given: a=8,c=5,B=40∘a=8,c=5,B=40∘ b2=a2+c2−2ac⋅cos(B)b2=a2+c2-2ac⋅cos(B) b2=82+52−2(8)(5)cos(40)b2=82+52-2(8)(5)cos(40) b2=27.7164b2=27.7164 b=5.26b=5.26 cos(A)=b2+c2−a22bccos(A)=b2+c2-a22bc cos(A)=5.262+52+822⋅5.26⋅5cos(A)=5.262+52+822⋅5.26⋅5 cos(A)=−.2144cos(A)=-.2144…