Question

While sailing, Jacob is 150 feet from a lighthouse. The angle of elevation from his feet on the boat (at sea level) to the top of the lighthouse is 48°

What can you conclude about the height of the lighthouse, with respect to Jacob's distance from the lighthouse? Explain your answer.

Answer 1

The height of the lighthouse is approximately 42.

Explanation:

This situation forms a right triangle so the angles would be 90 and 48

90+48+x=180

138+x=180

x=180-138

x=42

Answer 2

The height of the lighthouse is approximately 166.6 feet.

Explanation:

Let the height of the lighthouse be represented by s, then;

Tan 48° = (opposite) ÷ (adjacent)

Tan 48° = s ÷ 150

⇒ s = 150 × Tan 48°

= 150 × 1.1106

= 166.59

s ≅ 166.6 feet

Therefore, the height of the lighthouse is approximately 166.6 feet.