SOLUTION: A building 220 feet tall casts a 100 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the v

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Question 192748: A building 220 feet tall casts a 100 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.)
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


We'll see the man standing on the building.
---> This does not make sense, being 220ft tall building only casting 100ft shadow.

*Remember, the shadow serves as the hypotenuse, and is equal to the sq.root of the sum of the squares of the two sides. Being the building 220 ft tall is impossible.

*In a Right Triangle, the hypotenuse is always the longest side.

If you add another "0" on the length of the shadow, making 1000 ft on a 220ft tall building, then we can solve by Trigo function.

Solving by Trigo Function:
sin%28sigma%29=opp%2Fhyp
sin%28sigma%29=220ft%2F1000ft
sigma=sin%5E%28-1%29%28220%2F1000%29
red%28sigma=12.7%5Eo=13%5Eo%29 ---> This is the angle between the end of the shadow and the ground.

For the Angle between the shadow and the vertical side of the building:
180=90%2Bsigma%2Bbeta
180=90%2B13%5Eo%2Bbeta
beta=180-90-13
red%28beta=77%5Eo%29, Answer

Thank you,
Jojo