Answer to Question #2722 in Abstract Algebra for Saman khan

Question

A point O is at the top of a vertical cliff. The angle of elevation of O from a boat which is at a point A due South of O is 28°. The boat now sails 50 metres due North to a point B from which the angle of elevation of O is 70°. Find, to the nearest metre, the distance of B from the foot of the cliff.

Answer 1

<img src="../../..//assignments/uploaded_files/static/bb/bb/bbbb6df4fed880c2bdcb3f5e94bda2a6.png" title="" alt="">
We have the following picture.
Express h from left side and right side triangles:
h = a tan 70 = (50-a) tan 28,

whence
a =& (50 tan 28)/(tan 70+tan 28) = 8.11m