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25 votes
25 votes
S. Mr. Watkins looks up at the top of a tree. The tree is 10 m away, and he can see the top at an

angle of 25 degrees. How tall is the tree?

User Echiban
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1 Answer

13 votes
13 votes

The problem does not mention the height of S. Mr. Watkins, so we are just going to assume its from his feet.

So, i made this drawing to represent him and the tree, at a distance of 10 meters looking up at a 25* angle.

I marked the opposite side, adjacent side, and hypotenuse.

x is angle where you are "looking" from. I.E., from the POV of mr watkins.

sin(x) = opposite/hyp

cos(x) = adj/hyp

tan(x) = opp/adj

So, we have an unknown side which is the opposite side, represented by length x.

The side adjacent is 10 meters.

The angle from him is 25 degrees.

What deals with adjacent and opposite? Tangent.

Tan(25) = x/10

Solve for x.

10tan(25) is the height of the tree = 4.66

The height of the tree is 5 meters.

User Rens Tillmann
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