In a right triangle, one of the acute angles measures 30^ and the hypotenuse has length 14. What is the length of the side opposite the 30^ angle?

SAT Right triangles and trigonometry Practice Question 6 (Easy)

Question bank / Right triangles and trigonometry

Math · Geometry and TrigonometryEasy

In a right triangle, one of the acute angles measures $30^\circ$ and the hypotenuse has length $14$ . What is the length of the side opposite the $30^\circ$ angle?

$7$

$7\sqrt{3}$

$14\sqrt{3}$

$28$

Show answer and explanation

Answer: A

In a $30^\circ$ - $60^\circ$ - $90^\circ$ triangle, the side opposite the $30^\circ$ angle is half the hypotenuse. So the side has length $\frac{14}{2} = 7$ . This also follows from $14 \sin 30^\circ = 14 \cdot \frac{1}{2}$ .

Choice B is the length of the side opposite the $60^\circ$ angle.

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