Answer:
- 2904.7 yards from "one end"
- 2977.9 yards from "the other end"
Explanation:
You want the side lengths of a triangle with one angle of 82° and the other angle of 75° on either end of a side of length 1175 yards.
Sine law
The angle opposite the given side is ...
180° -82° -75° = 23°
The Law of Sines tells us the side lengths are proportional to the sine of the opposite angle. The middle-length side, opposite the 75° angle, has length ...
(1175 yd)·sin(75°)/sin(23°) ≈ 2904.7 yd . . . . from one end
The longest side, opposite the largest angle, is ...
(1175 yd)·sin(82°)/sin(23°) ≈ 2977.9 yd . . . . from the other end
The two distances to the platform are 2904.7 yd and 2977.9 yd.
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Additional comment
The platform is about 2876.4 yd from the beach.
We don't have the figure, so we have assumed an acute triangle in which each angle is measured between the platform and the other end of the beach.