Question

special right triangles quick check
if the side opposite a 60 - degree angle in a 30 - 60 - 90 right triangle is $7sqrt{3}$ cm long, how long is the hypotenuse? (1 point)
$\bigcirc$ 7 cm
$\bigcirc$ 28 cm
$\bigcirc$ 14 cm
$\bigcirc$ $7sqrt{3}$ cm

Explanation:

Step1: Recall 30-60-90 triangle ratios

In a 30-60-90 right triangle, the side opposite the 60° angle is $\frac{\sqrt{3}}{2}$ times the hypotenuse $c$. The relationship is:
$$\text{Side opposite }60^\circ = \frac{\sqrt{3}}{2}c$$

Step2: Substitute given value and solve for $c$

Substitute the given side length $7\sqrt{3}$ into the formula:
$$7\sqrt{3} = \frac{\sqrt{3}}{2}c$$
Multiply both sides by 2:
$$14\sqrt{3} = \sqrt{3}c$$
Divide both sides by $\sqrt{3}$:
$$c = 14$$

Answer:

14 cm (the option: 14 cm)