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Tamara wants to calculate the height of a tree outside her home. Using her clinometer (angle measuring device) she measures the angle from 35 feet away from the base of the tree and gets an angle of 62 degrees Tamara's eye level is 5.5 feet above the ground.


1. What trigonometric relationship (sine, cosine or tangent) would be used to determine how tall the tree is?

2. Write an equation to determine how tall the tree is, in feet.

3. How tall is the tree, in feet? Round your answer to the nearest tenth.

4. Marcus lives across the street from Tamara Marcus's eye-height is 4.25 feet, and he estimates that he views the top of the tree with an angle of elevation of 50 degrees and is standing 65 feet away from the tree. Are Marcus's estimates reasonable? Explain why or why not.

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Answer:

61.922 feet

Step-by-step explanation:

For this problem, we simply want to set up a trigonometric function that computes the height of the tree, and we want to add the height of Tamara.

We are given a distance from the tree of 30 feet with an angle from her eye-level to the top at 62 degrees.  So we can say the following:

y = tan(Θ) * x

Where Θ = 62 degrees, x = 30 feet, and y is the height of the tree from Tamara's eye level.

y = tan(Θ) * x

y = tan(62) * 30

y = 56.422

So we also need to include the height of Tamara to get the total height of the tree from the ground to the top.

56.422 ft + 5.5 ft = 61.922 ft

Hence, the total height of the tree is 61.922 feet.

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