Question

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) $7sqrt{3}$ cm 7 cm 14 cm 28 cm

Explanation:

Step1: Recall 30-60-90 triangle ratios

In a 30-60-90 right triangle, the sides are in the ratio \(1 : \sqrt{3} : 2\), where the side opposite 30° is \(x\), opposite 60° is \(x\sqrt{3}\), and hypotenuse is \(2x\).

Step2: Identify given side

The side opposite 60° is \(7\sqrt{3}\) cm. From the ratio, this side is \(x\sqrt{3}\). So, set \(x\sqrt{3}=7\sqrt{3}\).

Step3: Solve for x

Divide both sides by \(\sqrt{3}\): \(x = 7\).

Step4: Find hypotenuse

Hypotenuse is \(2x\), so substitute \(x = 7\): \(2\times7 = 14\) cm.

Answer:

14 cm