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

Answer:

16

Step-by-step 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 $\theta$:

$tan\theta=\frac{oppositeside}{adjacentside}=\frac{b}{a}$   (1)

$tan\theta=\frac{34m}{122m}$   (2)

$tan\theta=0.278$   (3)

$\theta={tan}^{-1} (0.278)$   (4)

Finally:

$\theta=15.572\°$