Find the height of the pole

Question

a tree sits on top of a tall building. An observer on the ground 17 m away from the building finds the angle of elevation to the base of the tree to be 30° And the angle of elevation to the top of the tree is 45°. Find the height of the tree to the nearest tenth of a meter. Draw a picture. 

Answer 1

To solve this problem without calculation you need to know that an in an isosceles right triangle, which has base angles of 45° each, the ratio of the sides to the hypotenuse is 1:1:√2 and in a 30-60 right triangle the similar ratio 1:√3:2, where the "1" side is opposite the 30° angle.

 

For this problem that means the height of the tree off the ground is 17m and the base of the tree is 17/√3 of the ground and the eight of the tree is 17[1 - (1/3)√3].  I will leave the arithmetic to you.