Question

Consider a triangle ABC like the one below. Suppose that A = 30°, B = 125°, and a = 38. (The figure is not drawn to scale.) Solve the triangle.

Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".

Answer 1

C = 25°, b = 62.3, c = 32.1

Explanation:

The Law of Sines can be used to solve a triangle when two angles and a side opposite one of them is given.

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third angle

The angle sum theorem can be used to find the third angle.

C = 180° -A -B = 180° -30° -125° = 25°

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unknown sides

The Law of Sines tells you ...

a/sin(A) = b/sin(B) = c/sin(C)

b = a(sin(B)/sin(A)) = 38·sin(125°)/sin(30°) ≈ 62.3

c = a(sin(C)/sin(A)) = 38·sin(25°)/sin(30°) ≈ 32.1

The solution is ...

C = 25°, b = 62.3, c = 32.1