if the side opposite a 60-degree angle in a 30-60-90 right triangle is 7sqrt3 cm long, how long is the hypotenuse

Answer 1

In a 30-60-90 right triangle, the ratios of the sides are as follows:

- The side opposite the 30-degree angle is x.
- The side opposite the 60-degree angle is x * sqrt(3).
- The hypotenuse is 2x.

Given that the side opposite the 60-degree angle is 7 * sqrt(3) cm long, we can set up the equation:

x * sqrt(3) = 7 * sqrt(3)

By dividing both sides of the equation by sqrt(3), we get:

x = 7

Therefore, the hypotenuse is 2x = 2 * 7 = 14 cm long.