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19 votes
A tree 10 meters high casts a 17.3 meter shadow. Find the angle of elevation to the sun

User Ding Peng
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1 Answer

28 votes
28 votes
Answer:
30.03 degrees

Explanation:

You have labeled this diagram correctly.

The trig function that links the side opposite the angle x and the length of the shadow is the tangent function.

Here, tan x = (opposite side) / (adjacent side) = (10 m) / (17.3 m), or 0.578.

Starting from tan x = 0.578, use the inverse tangent function to find the angle, first in radians and then in degrees:

arctan 0.578 = 0.524 radians

Converting this to degrees yields 30.03 degrees. This is the angle of elevation of the sun from the horizontal, from the point where the observer is standing.
User Wtekiela
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