Question

a tower stands on the top of a cliff. at a distance of 55m from the foot of the cliff, the angles of elevation of the top of the tower as well the cliff are 60° and 45° respectively. find the height of the tower.

Answer 1

as usual, draw a diagram. You will see that the distances to top and bottom of tower are

top/55 = tan 60°
bottom/55 = tan 45°

Now just evaluate top and bottom, and you can subtract to get the height of the tower.

You should get 55(√3 - 1)