The angle of elevation to a nearby tree from a point on the ground is measured to be 54degrees∘. How tall is the tree if the point on the ground is 89 feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary.
We can use trigonometry to solve this problem. Let's call the height of the tree $h$. Then we can set up the following equation based on the angle of elevation and the distance from the point on the ground to the bottom of the tree:
$$\tan(54^\circ) = \frac{h}{89}$$
To solve for $h$, we can multiply both sides of the equation by 89:
$$89\tan(54^\circ) = h$$
Using a calculator, we find that $\tan(54^\circ) \approx 1.376381920471173$. Therefore:
$$89\times 1.376381920471173 \approx 122.51385535269724$$
Rounding to the nearest hundredth of a foot, the height of the tree is approximately 122.51 feet.