Question

A kite flier wondered how high her kite was flying. She used a protractor to measure an angle of 15∘ from level ground to the kite string. If she used a full 50 yard spool of string, how high, in feet was the kite? (Disregard the string sag and assume that the string reel was at ground height.) Include units in your answer. All trig functions will be evaluated in degrees.

Answer 1

Answer:

12.9 yd

Step-by-step explanation:

It helps if you draw a triangle. Draw a horizontal segment. That is the ground. Now at the left end start a new segment that goes up to the right at approximately 15 degrees until it its other endpoint directly above the right endpoint of the horizontal segment. Connect these two endpoints. The vertical side on the right shows the height of the kite. The hypotenuse is the string.

For the 15-deg angle, the height of the triangle is the opposite leg, and the string is the hypotenuse. The trig ratio that relates the opposite leg tot he hypotenuse is the sine.

$\sin A = \dfrac{opp}{hyp}$

$\sin 15^\circ = \dfrac{h}{50~yd}$

$(50~yd)\sin 15^\circ = h$

$h = (50~yd)(0.2588)$

$h = 12.9~yd$