Question

A man was parasailing above a lake at an angle of elevation of 32° from a boat, as modeled in the diagram, If 129.5 meters of cable connected the boat to the parasail, approximately how many meters above the lake was the man? (1) 68.6 (2) 80.9 (3) 109.8 (4) 244.4

Non-right triangles and trigonometry
ANSWERED
asked 2020-10-21
A man was parasailing above a lake at an angle of elevation of 32° from a boat, as modeled in the diagram, If 129.5 meters of cable connected the boat to the parasail, approximately how many meters above the lake was the man?
(1) 68.6
(2) 80.9
(3) 109.8
(4) 244.4

Answers (1)

2020-10-22
Let x be the height of the man above the lake.
Since x is the side opposite the given angle and the cable is the hypotenuse, we use the skine ratio:
\(\displaystyle{\sin{{32}}}°={o}{p}\frac{{p}}{{a}}{d}{j}=\frac{{x}}{{129.5}}\)
\(\displaystyle{129.5}{\sin{{32}}}°={x}\)
x≈68.6 m
So, the answer is choice (1).
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