SOLUTION: Please help me solve this Trig question From the top of the cliff 250m high, Elizabeth sees 2 boats, one directly behind the other heading for shore. The angle of depression t

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me solve this Trig question From the top of the cliff 250m high, Elizabeth sees 2 boats, one directly behind the other heading for shore. The angle of depression t      Log On


   

Question 1127938: Please help me solve this Trig question

From the top of the cliff 250m high, Elizabeth sees 2 boats, one directly behind the other heading for shore. The angle of depression to the boat farther away from Elizabeth is 57 deg. the angle of depression to the nearer boat is 68deg calc. distance between two boats
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the cliff 250m+ high
the angle of depression to the boat farther away from Elizabeth is 57 degrees,
its angle of elevation is the same
you need to find the length of the horizontal leg of the triangle
use tan+%2857%29+=+250m%2Fx, which when solved for x is
x=250%2Ftan%28+57%29
x=250%2F1.54
x=162.34m
and the angle of depression to the nearer boat is 68deg
tan+%2868%29+=+250m%2Fx, which when solved for x+is
x=250%2Ftan%28+68%29
x=250%2F2.48
x=100.81m
distance between two boats is: d=162.34m-100.81m=61.53m