From a point 25.4 m from the base, a surveyor uses a theodolite and measures the angle of elevation to the top of the cliff as 72.5 degrees.What is the height of the cliff?

1 Answer | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The surveyor measures the top of the cliff from a point that lies at a distance of 25.4 m from the base of the cliff. The angle of elevation of the top of the cliff is 72.5 degrees.

If the height of the cliff is taken to be H, tan 72.5 = H/25.4

=> H = 25.4*tan 72.5

=> H = 80.55

The height of the cliff is 80.55 m

We’ve answered 318,916 questions. We can answer yours, too.

Ask a question