The angle of elevation to a nearby tree from a point on the ground is measured to be 53degrees ∘ . 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.Answer
Question
The angle of elevation to a nearby tree from a point on the ground is measured to be 53degrees ∘ . 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.Answer
Solution
To solve this problem, we can use the tangent of the angle of elevation, which is the ratio of the opposite side (the height of the tree) to the adjacent side (the distance from the tree).
The formula for tangent is:
tan(θ) = opposite/adjacent
We know the angle of elevation (θ) is 53 degrees and the distance from the tree (adjacent) is 89 feet. We want to find the height of the tree (opposite). So we can rearrange the formula to solve for the opposite side:
opposite = tan(θ) * adjacent
Substitute the given values into the formula:
Height of tree = tan(53) * 89
Now, calculate the tangent of 53 degrees and multiply it by 89.
After calculating, you will get the height of the tree. Remember to round your answer to the nearest hundredth of a foot if necessary.
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