Question bank / Right triangles and trigonometry

Math · Geometry and TrigonometryMedium

A kite is flying at the end of a straight string that is 120120 feet long. The other end of the string is tied to a stake in the ground, and the string makes a 60∘60^\circ angle with the level ground. How many feet above the ground is the kite?

A

6060

B

60260\sqrt{2}

C

60360\sqrt{3}

D

1203120\sqrt{3}

Show answer and explanation

Answer: C

The string, the ground, and the kite's height form a right triangle with a 60∘60^\circ angle at the stake. The height is opposite the 60∘60^\circ angle, and the 120120-foot string is the hypotenuse. So the height is 120sin⁡60∘=120⋅32=603120 \sin 60^\circ = 120 \cdot \frac{\sqrt{3}}{2} = 60\sqrt{3} feet.

Choice A is the side opposite the 30∘30^\circ angle, which is the horizontal distance from the stake to the point directly below the kite, not the kite's height.

Why the other choices are wrong

  • A. 60 is the side opposite the 30 degree angle, the horizontal distance along the ground.
  • B. This uses a 45 degree angle, but the string makes a 60 degree angle with the ground.
  • D. This treats the string as the leg next to the angle and uses tangent, but the string is the hypotenuse.
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