Question

You are standing 40 meters from the base of the 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°50, what is the height of the tree?

Answer 1

height of the tree `~~16.24m`

Explanation:

Let `B and T` be the base and the top of the tree, respectively, as shown in the figure.
`20^@50'=20+50/60=20.833^@`
`=> angleBTA=180-98-20.833=61.167^@`
by the law of sines, we get:
`(BT)/sin20.833=40/sin61.167`

`=> BT=40*(sin20.833)/(sin61.167)~~16.24` m