Question

A boat is 122 meters from the base of a lighthouse that is 34 meters above sea level. What is the angle of elevation from the boat to the top of the lighthouse? Round to the nearest degree.

Answer 1

16

Explanation:

A boat is 122 meters from the base of a lighthouse that is 34 meters above sea level. What is the angle of elevation from the boat to the top of the lighthouse? Round to the nearest degree.

Answer 2

Answer:
`15.57\°`

In order to understand better this problem, we can use the figure attached, in which we have a right triangle (with a 90 degree angle), where
`c` is its hypotenuse,
`a` is the adjacent side to the angle of elevation
`\theta` from the boat to the top of the lighthouse and
`b` is the opposite side to
`\theta`.

Knowing this, we will use the tangent trigonometric function to find
`\theta`:

`tan\theta=(oppositeside)/(adjacentside)=(b)/(a)` (1)

`tan\theta=(34m)/(122m)` (2)

`tan\theta=0.278` (3)

`\theta={tan}^(-1) (0.278)` (4)

Finally:

`\theta=15.572\°`