Question

bird is flying directly above a tree you are standing 40 feet away from the tree the angle of elevation to the top of the tree is 32 degrees and the angle of elevation to the bird is 42° how far above the tree is the bird

Answer 1

Answer: 11 ft

Step-by-step explanation:

Given

The boy is standing 40 feet away from the tree

the angle of elevation for the tree is $32^{\circ}$

the angle of elevation for the bird is $42^{\circ}$

using figure

$\frac{h+x}{40}=\tan 42^{\circ}\\h+x=40\tan 42^{\circ}\ldots (i)\\Now,\\\tan 32^{\circ}=\frac{h}{40}\\h=40\tan 32^{\circ}$

Put the value of h in equation (i)

$40\tan 32^{\circ}+x=40\tan 42^{\circ}\\x=40[\tan 42^{\circ}-\tan 32^{\circ}]\\x=40[0.9-0.624]=0.276\times 40=11.04\ ft$