Answer:
Height of the light house is 120 feets
Explanation:
From the picture above the lighthouse and the human cast there shadow in the same direction and on the same horizontal surface. so, both are likely to get the same angle of depressions.
Translating the events mathematically, both formed a right angle triangle . The first triangle has only base/adjacent length, so you need an angle to get the height as required from the question. The second triangle has two sides known so we can use the known sides to get the angle of depression which can be use to get the height of the first triangle.
Now let's get the angle of the second triangle .
using SOHCAHTOA,
since we are given the opposite and adjacent length of the triangle we use
tan ∅ = opposite/adjacent = 5.5/2.2 = 2.5
tan ∅ = 2.5
Now the angle of depression is already known let us use it to solve for the height in the first triangle .
tan ∅ = opposite/adjacent = height/48
Recall tan ∅ = 2.5
Therefore 2.5 = height/48
cross multiplying
2.5 × 48 = height
height = 120 feets