Question

a yacht is anchored 90 feet offshore from the base of a lighthouse. the angle of elevation from the boat to the top of the lighthouse is 26 degrees. the distance between the yacht and the top of the lighthouse is about 100 feet. which of these is nearest to the height of the lighthouse?
135 feet
45 feet
110 feet
25 feet

Explanation:

Step1: Define trigonometric relation

We use the tangent function, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta=26^\circ$, adjacent side = 90 ft, opposite side = height of lighthouse ($h$).

Step2: Isolate height variable

Rearrange to solve for $h$: $h = 90 \times \tan(26^\circ)$

Step3: Calculate numerical value

Using $\tan(26^\circ) \approx 0.4877$, we get:
$h \approx 90 \times 0.4877 = 43.893$ ft

Answer:

B. 45 feet