Question

Consider a triangle ABC like the one below. Suppose that a = 47, b = 59, and A = 37" (The figure is not drawn to scale.) Solve the triangle,

Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or",

Answer 1

B = 49.1°

C = 93.9°

c = 77.9

Explanation:

Given:

a = 47, b = 59, and A = 37°

Required:

B, C, and c

Solution:

✔️To find B, apply the law of sines:

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

Plug in the values

`(sin(37))/(47) = (sin(B))/(59)`

Cross multiply

`47*sin(B) = sin(37)*59`

Divide both sides by 47

`(47*sin(B))/(47) = (sin(37)*59)/(47)`

`sin(B) = 0.7555`

`B = sin^(-1)(0.7555)`

`B = sin^(-1)(0.7555)`

B = 49.0690779° ≈ 49.1° (nearest tenth)

✔️C = 180° - (A + B) (sum of triangle)

C = 180° - (37° + 49.1°)

C = 93.9°

✔️To find c, apply the law of sines:

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

Plug in the values

`(sin(49.1))/(59) = (sin(93.9))/(c)`

Cross multiply

`c*sin(49.1) = sin(93.9)*59`

Divide both sides by sin(49.1)

`c = (sin(93.9)*59)/(sin(49.1))`

c = 77.8766982

c ≈ 77.9 (nearest tenth)