A light house operator is 34m above sea level. He spots a sailboat in the distance. The angle of depression of the sighting is 1
0. How far is the boat from the base of the lighthouse?
1 answer:
Answer: the distance of the boat from the base of the lighthouse is 192.9 m
Step-by-step explanation:
The scenario is represented in the right angle triangle shown in the attached photo.
Looking at triangle ABC, the height of the light house operator above sea level represents the opposite side of the right angle triangle.
Angle A = 10° because it is alternate to the angle of depression.
To determine AB, the distance of the boat from the base of the lighthouse, we would apply
the tangent trigonometric ratio which is expressed as
Tan θ, = opposite side/adjacent side. Therefore,
Tan 10 = 34/AB
AB = 34/Tan 10 = 34/0.1763
AB = 192.9 m
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