You are standing 40 meters from the base of a tree that is leaning 8° from the vertical away from you.The angle of elevation from your feet to the top of the tree is 20°. Find the height of the tree.

Question

You are standing 40 meters from the base of a tree that is leaning 8° from the vertical away from you.The angle of elevation from your feet to the top of the tree is 20°. Find the height of the tree.

Answer 1

Once you have a labelled diagram, it is easy to see that the third angle is 62° (angle sum of a triangle = 180°)

Now use the Sine Rule to calculate x, the height of the tree:

x/sin20° = 40/sin62°

x = 15.5 m

Answer 2

Label all interior angles.

Use Law of Sines to determine length.