The angle of elevation to a nearby tree from a point on the ground is measured to be 49degrees ∘ . How tall is the tree if the point on the ground is 53 feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary.
Question
The angle of elevation to a nearby tree from a point on the ground is measured to be 49degrees ∘ . How tall is the tree if the point on the ground is 53 feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary.
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 49 degrees and the distance from the tree (adjacent) is 53 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(49 degrees) * 53 feet
Now, calculate the tangent of 49 degrees and multiply it by 53.
After calculating, you will find that the height of the tree is approximately 65.05 feet. So, the tree is about 65.05 feet tall.
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