Question

From a boat on the lake, the angle of elevation to the top of a cliff is 14°28'. If the base of the cliff is 743 feet from the boat, how high is the cliff (to the nearest foot)?

A.) 195 ft
B.) 192 ft
C.) 205 ft
D.) 202 ft

Answer 1

In order to solve the problem, it is best to draw the situation and we will see that it forms a right triangle. We use a trigonometric function for this case. We use the tangent function which is:

tan ∅ = opposite side / adjacent side

where ∅ is the angle of elevation of the boat to the top of the cliff, opposite side is the height of the cliff and adjacent side is the distance of the boat to the base of the cliff.

tan 14°28' = h / 743
h = 192 ft ===> Answer is B.