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 [tex]32^{\circ}\\[/tex]
the angle of elevation for the bird is [tex]42^{\circ}\\[/tex]
using figure
[tex]\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}[/tex]
Put the value of h in equation (i)
[tex]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[/tex]
