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.
To find the height of the tree, we can use trigonometry.
Let x be the height of the tree.
Using the tangent function, we have:
tan(54°) = x / 89
x = 89 * tan(54°)
x ≈ 89 * 1.3763819
x ≈ 122.508 feet
Therefore, the tree is approximately 122.51 feet tall.