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?25 feet45 feet135 feet110 feet

Explanation:

Step1: Define trigonometric relation

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

Step2: Rearrange to solve for $h$

$h = 90 \times \tan(26^\circ)$

Step3: Calculate the value

$\tan(26^\circ) \approx 0.4877$, so $h \approx 90 \times 0.4877 = 43.893$ ft

Answer:

45 feet