Answer: [tex]15.57\°[/tex]
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 [tex]c[/tex] is its hypotenuse, [tex]a[/tex] is the adjacent side to the angle of elevation [tex]\theta[/tex] from the boat to the top of the lighthouse and [tex]b[/tex] is the opposite side to [tex]\theta[/tex].
Knowing this, we will use the tangent trigonometric function to find [tex]\theta[/tex]:
[tex]tan\theta=\frac{oppositeside}{adjacentside}=\frac{b}{a}[/tex] (1)
[tex]tan\theta=\frac{34m}{122m}[/tex] (2)
[tex]tan\theta=0.278[/tex] (3)
[tex]\theta={tan}^{-1} (0.278)[/tex] (4)
Finally:
[tex]\theta=15.572\°[/tex]
