A light house operator is 34m above sea level. He spots a sailboat in the distance. The angle of depression of the sighting is 10. How far is the boat from the base of the lighthouse?

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

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

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