Question

A kite flying in the air has a 12 - ft line attached to it. its line is pulled taut and casts a 10 - ft shadow. find the height of the kite. if necessary, round your answer to the nearest tenth.

Answer 1

The height of the kite will be 6.6 ft rounded to the nearest tenth.

Explanation

According to the below diagram, AB is the height of the kite and AC is the 12 ft line attached to it.

The line is pulled taut and casts a 10 ft shadow. That means BC = 10 ft

Now, in right angle triangle ABC, using Pythagorean theorem....

$(AB)^2 +(BC)^2 = (AC)^2 \\ \\ (AB)^2 +(10)^2 = (12)^2 \\ \\ (AB)^2 +100 = 144\\ \\ (AB)^2 = 144-100 =44\\ \\ AB=\sqrt{44}= 6.6332....$

So, the height of the kite will be 6.6 ft rounded to the nearest tenth.