Question

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 18°33'. When the boat stops, the angle of depression is 51°33'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

Answer 1

437.21

Explanation:

1) Convert 18 degrees 33/60--> 18.55

51 degrees 33/60--> 51.55

*Use 60 because theres 60 seconds in a minute

2) Subtract 90-18.55= 71.45

90- 51.55= 38.45

*90 because it's a right triangle

3) Tan (18.55)=200/x

tan(38.45)=x/200

*When you do it make sure you do tan first if you don't you arent going to get the right answer (found that out the hard way)

4) Plug in what you got for both answers (from step three) to subtraction.

596. 007998- 158.802416= 437.205582

5) Round to the hundredths

437.21

Answer 2

tan(51 33')= 200/base1
base1= 158.802

tan(18 33')=200/base2
base2=596.008

The distance travelled=596.008-158.802 =438m