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A sailor sights both the bottom and top of a lighthouse that is 20m high and stands on the wedge of a cliff. The two angles of elevation are 35 degrees and 42 degrees. To the nearest meter, how far is the boat from the cliff?

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Kaizoku00id
use tangent to solve this problem

let d the distance of the boat

first let solve the x for the height of 35 degrees elevation
and in terms it in d
tan35 = x/d
x = dtan35

then for the 42 degree
and the opp of this situation is the sum of the height of the lighthouse plus x, and we have the value of x
so the equation become
tan42 = (20 + dtan35) /d
solving more by algebra
you will get
d = 99.9 m far the boat from the cliff







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