The length of a string between a kite and a point on the ground is 90 m. If
the string is making an angle with the level ground such that tan =
15/8, how high will the kite be ?

In this problem we deal with a right triangle with hypotenuse 90 m. We are told that tan Ф = 15/8; 15 represents the vertical distance of the kite off the ground and 8 represents the horizontal distance from the kite flyer to the kite. This is sufficient info from which to determine the angle of elevation from kite flyer to kite: tan Ф = 15/8 yields Ф = 1.08 radians.

Using this same angle Ф = 1.08 radians, sin Ф = (vertical distance) / hypotenuse = sin 1.08 rad = 0.882.

Then the vertical distance (height of the kite) is

(90 m)(0.882) = 79.4 m

The length of a string between a kite and a point on the ground is 90 m. If the string is making an angle with the level ground such that tan = 15/8, how high will the kite be ?

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The length of a string between a kite and a point on the ground is 90 m. If
the string is making an angle with the level ground such that tan =
15/8, how high will the kite be ?