Question

An ant looks up to the top of a tree with an angle of elevation of 38. if the ant is 43 feet from the base of the tree, what is the height of the tree, to the nearest tenth?

a. 33.6 feet
b. 34.1 feet
c. 35.4 feet
d. 38.5 feet

Answer 1

The answer to this question is:

An ant looks up to the top of a tree with an angle of elevation of 38. if the ant is 43 feet from the base of the tree, what is the height of the tree, to the nearest tenth?
"33.6 Ft"

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Answer 2

33.6 feet

Explanation:

Given : An ant looks up to the top of a tree with an angle of elevation of 38.

To Find: If the ant is 43 feet from the base of the tree, what is the height of the tree, to the nearest tenth?

Solution:

Refer the attached figure

An ant looks up to the top of a tree with an angle of elevation of 38.i.e.∠ACB= 38°

The ant is 43 feet from the base of the tree i.e.BC = 43 feet.

Now we are supposed to find the height of the tree i.e. AB

Now we will use trigonometric ratio

`Tan \theta = (Perpendicular)/(Base)`

`Tan 38^(\circ) = (AB)/(BC)`

`Tan 38^(\circ) = (AB)/(43)`

`0.78128= (AB)/(43)`

`0.78128 * 43= AB`

`33.6= AB`

Hence the height of the tree is 33.6 feet.