Question

Find the height of the tree to the nearest foot.

Answer 1

• Height be x

`\\ \rm\Rrightarrow tan\theta=(Perpendicular)/(Base)`

`\\ \rm\Rrightarrow tan34.6=(x)/(72)`

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

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

`\\ \rm\Rrightarrow x=49.61ft`

• height approximately 50ft

Answer 2

height = 50 ft (nearest foot)

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=(opposite \ side)/(adjacent\ side)}`

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

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

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