Question

HELP PLS! A boat is heading towards a lighthouse, whose beacon-light is 102 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 13^{\circ}

, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 22^{\circ}

. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.

Answer 1

Distance from point AA to point BB = 189.3 feet

Explanation:

Let the distance from point AA to the base of the lighthouse be represented by x, and the distance from point BB to the base of the lighthouse be represented by y. So that;

distance from point AA to point BB = x - y

To determine the value of x, applying the required trigonometric function;

Tan θ =
`(opposite)/(sdjacent)`

Tan 13 =
`(102)/(x)`

x =
`(102)/(Tan 13)`

= 441.81 feet

x = 441.8 feet

To determine the value of y;

Tan 22 =
`(102)/(y)`

y =
`(102)/(Tan 22)`

= 252.46

y = 252.5 feet

Thus,

distance from point AA to point BB = 441.8 - 252.5

= 189.3 feet