Question

A yathc is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. What is nearest to the hieght of the lighthouse

Answer 1

44 ft

Explanation:

The set up will give a right angled triangle where;

Base of the triangle = 90 ft (distance of the offshore from the base of the house)

theta = 26 degrees (angle of elevation)

Height of the house will be the opposite side = x

Using the TOA trig identity;

tan 26 = opp/hyp

tan 26 x/90

x = 90tan 26

x = 90(0.4877)

x = 43.89 ft

Hence the nearest height of the house is 44ft