Answer:
∠T ≈ 22.7°
Explanation:
You want the measure of ∠T in ∆STU, given t = 130 cm, s = 300 cm, and ∠S = 117°.
Law of sines
The law of sines can be used to solve a triangle when two angles and at least one side are given. Here, it tells us ...
sin(T)/t = sin(S)/s
T = arcsin((t/s)sin(S)) = arcsin(130/300·sin(117°)) ≈ 22.7°
The measure of angle T is about 22.7°.
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Additional comment
When one acute angle is given and it is opposite the shortest side, there may be two possible solutions to the triangle. Here, the obtuse angle is opposite the longest side, so there can be only one solution to the triangle.
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