Answer :
We know that
• The angle of elevation is 25 degrees.
,• The ship is 1500 meters from the lighthouse.
Let's make a diagram to visualize the problem.
Where x represents the height of the lighthouse. Let's use a trigonometric reason to find x.
In this case, it's convenient to use the tangent reason.
[tex]\tan \theta=\frac{\text{opposite leg}}{adjacent\text{ leg}}[/tex]The opposite leg is x, the adjacent leg is 1500, and the angle is 25.
[tex]\tan 25=\frac{x}{1500}[/tex]To solve for x let's multiply each side by 1500.
[tex]\begin{gathered} 1500\cdot\tan 25=1500\cdot\frac{x}{1500} \\ x\approx699.5m \end{gathered}[/tex]Therefore, the lighthouse is 699.5 meters tall.
