Question

find the height of the tree to the nearest foot.

Answer 1

Answer:

height = 50 ft (nearest foot)

Step-by-step explanation:

This creates a right triangle, where:

• horizontal leg = 72 ft
• vertical leg = height of tree
• angle of elevation (between horizontal leg and hypotenuse) = 34.6°

Use the tan trig ratio to find the height.

$\mathsf{\tan\theta=\dfrac{opposite \ side}{adjacent\ side}}$

$\implies \mathsf{\tan(34.6)=\dfrac{height}{72}}$

$\implies \mathsf{height=72\tan(34.6)}$

$\implies \mathsf{height=50 \ ft \ (nearest\ foot)}$

Answer 2

• Height be x

$\\ \rm\Rrightarrow tan\theta=\dfrac{Perpendicular}{Base}$

$\\ \rm\Rrightarrow tan34.6=\dfrac{x}{72}$

$\\ \rm\Rrightarrow x=72tan34.6$

$\\ \rm\Rrightarrow x=72(0.689)$

$\\ \rm\Rrightarrow x=49.61ft$

• height approximately 50ft