A cliff measures 85 feet above the sea. The angle of depression of a boat measures 43 degrees from the top. How far is the boat from the base of the cliff?

Question

Advanced Mathematics

Answer 1

I believe a relationship such as tan(47°)= x/85 would solve your problem for you.

 

I believe your problem is similar to problem 4 on this website.

 

http://geometry--20-p6-yrh-b.patrioths.schools.pwcs.edu/modules/locker/files/get_group_file.phtml?gid=4714552&fid=27298834

Answer 2

Height of the cliff = h = 85 feet,   angle of depression = ∝ = 43 degs., Draw triangle ABC, such that angle ABC = 90deg

A_____________________________

I\

I  \          

I    \ 

I      \

I        \                   angle CAD = 43 deg,  so angle CAB = 90 - 43 = 47 degs

I______\

B          C              tan 47 = BC / AB

 

                           1.07235  = BC / 85

 

                            BC  =  1,07235 * 85

 

                            BC  =  91.15 feet

 

    Distance of boat from the cliff is 91.15 feet