Answer:
- u = 8.8
- V = 75.6°
- W = 63.4°
Step-by-step explanation:
You want the solution to triangle UVW, given U=41°, v=13, w=12.
Law of cosines
When two sides and the angle between them are known, the law of cosines can be used to find the third side.
u² = v² +w² -2vw·cos(U)
u = √(v² +w² -2vw·cos(U)) = √(13² +12² -2·13·12·cos(41°)) ≈ √77.5306
u ≈ 8.8
Law of sines
The law of sines can be used to find another angle:
sin(V)/v = sin(U)/u
V = arcsin(v/u·sin(U)) = arcsin(13/8.80515·0.65606) ≈ 75.6°
W = 180° -41° -75.6° = 63.4° . . . . . . . using angle sum theorem
The other sides and angles are u ≈ 8.8, V ≈ 75.6°, W ≈ 63.4°.
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Additional comment
Here, we have rounded to tenths. The attached calculator display shows the values to full calculator precision, so you can round them as your answer checker may require.
