Answer
The height of the building is\[126\text{ ft}\].
Work Step by Step
Angle of elevation is the angle made by the horizontal line and the line of sight to an object. As the angle of elevation opposite to the height of the transit above the ground and next to the eight from the building, use the tangent ratio formula as follows:
\[\tan \theta =\frac{a}{b}\]
where a is the side opposite to the angle and b is the side adjacent to the angle that is the distance of the ship from lighthouse. Here, b is\[300\text{ ft}\].
Compute the value a,as follows:
\[\begin{align}
& \tan 22{}^\circ =\frac{a}{300} \\
& a=300\times \tan 22{}^\circ \\
& =300\times 0.404 \\
& =121.20\text{ ft}
\end{align}\]
Compute the height of the building as shown below:
\[\begin{align}
& h=121.20\text{ ft}+5\text{ ft} \\
& =126.20\text{ ft} \\
& \approx 126\text{ ft}
\end{align}\]
