Answer:
40.45°
Explanation:
You want the angle opposite the side of length 13 ft in a triangle with the other sides being 16 ft and 20 ft.
Law of cosines
The law of cosines tells you ...
c² = a² +b² -2ab·cos(C)
Then angle C is ...
C = arccos((a² +b² -c²)/(2ab))
In the given triangle, this is ...
C = arccos((16² +20² -13²)/(2·16·20)) = arccos(487/640) ≈ 40.453°
The measure of angle θ is about 40.45°.
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