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Set 4

Question 18

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18

Number 18

A fishing boat moves from an initial position towards a pier for a distance of 2 km2\text{ km}. An observer on the boat sees the top of a hill with an elevation angle of 37∘37^\circ. The line-of-sight distance from the observer to the hilltop at the initial position is 12 km12\text{ km}. After the boat arrives at the pier, the elevation angle becomes 53∘53^\circ. What is the height of the hill?

Given:

sin⁡53∘=0.8→cos⁡53∘=0.6\sin 53^\circ = 0.8 \rightarrow \cos 53^\circ = 0.6
sin⁡37∘=0.6→cos⁡37∘=0.8\sin 37^\circ = 0.6 \rightarrow \cos 37^\circ = 0.8