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
14 cm
28 cm
7 cm

Explanation:

Step1: Recall the ratio of sides in 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, if the side opposite 30° is $x$, the side opposite 60° is $x\sqrt{3}$, and the hypotenuse is $2x$.

Step2: Find the value of $x$

Given the side opposite 60° is $7\sqrt{3}$. Since side opposite 60° = $x\sqrt{3}$, then $x\sqrt{3}=7\sqrt{3}$. Solving for $x$, we divide both sides by $\sqrt{3}$: $x = 7$.

Step3: Calculate the hypotenuse

The hypotenuse is $2x$. Substituting $x = 7$, we get hypotenuse = $2\times7=14$.

Answer:

14 cm