Tamara wants to calculate the height of a tree outside her home. Using her clinometer, she measures the slope angle from 30 feet away from the base of the tree and gets an angle of 62.
If Tamara's eye level is 5.5 feet above the ground, how tall is the tree? (Round your answer to the nearest hundredth)
Answer

The height of the tree is 61.92 feet.

Given information:

Tamara wants to calculate the height of a tree outside her home.

She is 30 ft away from the tree.

Tamara's eye level is 5.5 feet above the ground.

The angle of inclination of the top of the tree is 62 degrees.

Let h be the height of the tree.

See the attached image.

Use trigonometric ratios in triangle ABC to calculate the height of the tree as,

Therefore, the height of the tree is 61.92 feet.

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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.

Cheers.

step-by-step explanation:

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