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

Question

2 years ago

12

e the triangle.
Round your answers to the nearest tenth.
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1 answer:

Agata [3.3K] · Answer 1 · 2023-09-06T02:28:42+03:00

Answer:

C = 25°, b = 62.3, c = 32.1

Step-by-step 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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<h3>third angle</h3>

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

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

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<h3>unknown sides</h3>

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