Trigonometric Functions

Question

A 40 meter high tower stands vertically on a hillside sloping ground which makes an angle of 18 degrees wit the same horizontal. A tree also stands vertically up the hill from the tower. An observer on top of the tower finds the angle of depression of the top of the tree to be 26 degrees and the bottom of the tree to be 38 degrees. A)What is the height of the tree? B)Find the inclined distance bet the tower and the tree. C)What is the subtended angle of the tree at the base of the tower?

Answer 1

You absolutely cannot solve this problem without drawing a figure!!!!

Once you draw the figure, you can start filling in all the important angles by means of complementary angles, parallel lines and the sum of the angles in a triangle.

Then use the law of sines to get various lengths, such as the distance from the base of the tree to the base of the tower, the distance from the top of the tower to the base of the tree.

You will need the law of cosines to get the height of the tree.

Lots of computations! Good luck!