Question

2. An observer on top of a 50 foot tall lighthouse sees a boat at a 7 angle of depression. To the nearest foot how far is the boat from the base of the lighthouse ? A. 6 feet B. 50 feet C. 407 feet D. 410 feet

Answer 1

Answer:

The distance between the boat and the base of the lighthouse is:

C. 407 feet

Step-by-step explanation:

Given:

Height of lighthouse = 50 ft

Angle of depression from observer to boat = 7°

To find the distance of the boat from the base of the lighthouse.

Solution:

The situation can be represented by a right triangle ABC such that:

m∠ACB = $90\°-7\°$= 83°

BC= 50 ft

We need to find length of AB.

Applying trigonometric ratios.

$\tan\theta=\frac{AB}{BC}$

Plugging in given values.

$\tan83\°=\frac{AB}{50}$

$8.14=\frac{AB}{50}$

Multiplying both sides by 50

$50\times 8.14=\frac{AB}{50}\times 50$

$407=AB$

∴ $AB=407\ ft$

Thus, distance between the boat and the base of the lighthouse 407 feet