SOLUTION: An observer's eye is 6ft above the floor. The bottom of the mural is at floor level. The observer looks down 13 degrees to see the bottom and up 17 degrees to see the top. How tall

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Question 862905: An observer's eye is 6ft above the floor. The bottom of the mural is at floor level. The observer looks down 13 degrees to see the bottom and up 17 degrees to see the top. How tall is the mural?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This forms two right triangles. The lower triangle of the 13 degrees will let you find the distance from the observer's eye to the mural. The side opposite of the 13 degree angle is 6 feet. Draw that to understand more clearly.

Let d = distance from eye to the mural.
tan%2813%29=6%2Fd
d%2F6=1%2Ftan%2813%29
d=6%2Ftan%2813%29

Once you have the value for d, you are ready to use tangent of 17 degrees for the upper part of the mural, using the upper triangle. Assuming you now have a value for d,

Let v = the upper part of the mural which is distance from eye level to the top of the mural.
v%2Fd=tan%2817%29
v=d%2Atan%2817%29

You finally want, "how tall is the mural". This is d+v.
Tallness, d%2Bv
6%2Ftan%2813%29%2Bd%2Atan%2817%29
6%2Ftan%2813%29%2B%286%2Ftan%2813%29%29tan%2817%29
6%281%2Ftan%2813%29%2Btan%2817%29%2Ftan%2813%29%29
highlight%28%286%2Ftan%2813%29%29%281%2Btan%2817%29%29%29-----How tall the mural.

You could use any of these forms for the tallness you like.