A student is standing 20 feet away from the base of a tree. He looks to the top of the tree at a 50° angle
of elevation. His eyes are 5 feet above the ground. Using cos 50° 0.64, what is the height of the tree
to the nearest foot?

36 feet
29 feet
24 feet
31 feet

Answer:

[tex] \tan(50) =opp(x) \div adh(20) \\ \tan50 \times 20 = opp(h) \\ = 23.8 [/tex]

therefore the answer is 24

The height of the tree is approximately 26 feet.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

Let's denote the height of the tree with 'h'.

Then we can use the trigonometric ratio for cosine as follows:

cos(50°) = adjacent/hypotenuse

cos(50°) = 20/h + 5 (the adjacent side is the distance from the student's eyes to the tree, which is 20 feet, and the hypotenuse is the height of the tree plus the height of the student's eyes, which is h + 5 feet)

Now we can solve for 'h':

0.64 = 20/(h + 5)

0.64(h + 5) = 20

0.64h + 3.2 = 20

0.64h = 16.8

h = 26.25

So the height of the tree is approximately 26 feet (rounded to the nearest foot), which means the closest answer choice is 29 feet.

Therefore,

The height of the tree is approximately 26 feet.

Learn more about trigonometric identities here:

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