A man flies a kite with a 100 foot string. The angle of elevation of the string is 52°. How high off the ground is the kite?

Answer 1

The kite is approximately 78.80 feet off of the ground.

If we assume that the string his held taut without any swag, we can use a right triangle to solve for the height of the kite.

For this triangle with a reference angle of #52^o#, the hypoteneuse is #100ft# and the #h# is the height on the opposite side of the triangle from the reference angle.

Sine of an angle is the ratio of the opposite side over the hypotenuese.

#Sintheta = (opp)/(hyp)#

#sin52^o = h/(100ft)#

#100sin52^o = h#

#100(0.7880) = h#

#78.80ft =h#

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