Question

Solve the triangle. Round your answers to the nearest tenth. A. m∠A=43, m∠B=55, a=16 B. m∠A=48, m∠B=50, a=23 C. m∠A=48, m∠B=50, a=26 D. m∠A=43, m∠B=55, a=20

Answer 1

20.0

Explanation:

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Answer 2

D. m∠A=43, m∠B=55, a=20

Explanation:

Given:

∆ABC,

m<C = 82°

AB = c = 29

AC = b = 24

Required:

m<A, m<C, and a (BC)

SOLUTION:

Find m<B using the law of sines:

`(sin(B))/(b) = (sin(C))/(c)`

`(sin(B))/(24) = (sin(82))/(29)`

`sin(B)*29 = sin(82)*24`

`(sin(B)*29)/(29) = (sin(82)*24)/(29)`

`sin(B) = (sin(82)*24)/(29)`

`sin(B) = 0.8195`

`B = sin^(-1)(0.8195)`

`B = 55.0`

m<B = 55°

Find m<A:

m<A = 180 - (82 + 55) => sum of angles in a triangle.

= 180 - 137

m<A = 43°

Find a using the law of sines:

`(a)/(sin(A)) = (b)/(sin(B))`

`(a)/(sin(43)43) = (24)/(sin(55))`

Cross multiply

`a*sin(55) = 25*sin(43)`

`a = (25*sin(43))/(sin(53))`

`a = 20` (approximated)