Question

Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. B = 15° C = 113° b = 49

A = 50°, a = 174.3, c = 149.2

A = 52°, a = 151.2, c = 176.3

A = 52°, a = 149.2, c = 174.3

A = 50°, a = 176.3, c = 151.2

Answer 1

A = 52°, a = 149.2, c = 174.3

Explanation:

Technology is useful for this. Many graphing calculators can solve triangles for you. The attachment shows a phone app that does this, too.

___

The Law of Sines can give you the value of c, so you can choose the correct answer from those offered.

c = sin(C)·b/sin(B) = sin(113°)·49/sin(15°) ≈ 174.271 ≈ 174.3 . . . . . third choice

Answer 2

A = 52°, a = 149.2, c = 174.3

Explanation:

We are given the following two known angles and one known side length for a triangle and we are to find the rest of the side lengths and angle:

B = 15° C = 113° b = 49

A = 180 - ( 15 + 113) = 52°

For finding the side lengths, we can use the sine rule:

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

`(a)/(sin(52)) =(49)/(sin(15))`

a = 149.2

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

`(c)/(sin(113)) =(49)/(sin(15))`

c = 174.3