Question

Find the height of the tree to the nearest foot

Answer 1

Looking at the triangle, we see that the angle 29.7 deg and the "adjacent side" length 20 ft are given.  Our job is to find the "opposite side," which is the height of the tree.

Write out the tangent function:    tan 29.7 deg = opp side  /  adj side

Then tan 29.7 deg = (opp side) / (20 ft).

Solving for the length of the opp side:

opp side = (20 ft)(0.57) = 11.41 feet.  This is also the height of the tree.

Answer 2

Answer: b. 11 ft.

Step-by-step explanation:

In the given figure, it can be seen that the tree is standing vertical to the ground making right angle.

Using trigonometric ratio, we have

$\tan(29.7^{\circ})=\dfrac{\text{Perpendicular}}{\text{Base}}\\\\\Rightarrow\ \tan(29.7^{\circ})=\dfrac{h}{20}\\\\\Rightarrow 0.57038992967=\dfrac{h}{20}\\\\\Rightarrow\ h=0.5704\times20=11.408\approx11\text{ foot}$

Therefore, the height of the tree = 11 ft.