# Answer to Question #2722 in Abstract Algebra for Saman khan

Question #2722

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.

Expert's answer

<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

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

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