Question

Find the length of side x in simplest radical form with a rational denominator.

Answer 1

Answer: 10

Explanation:

a 30° - 60° - 90° triangle has a side ratio of 1:√3: 2, meaning the side length across from the 30° is 1, the side length across from 60° is √3, and the side length across from 90° is 2

if you multiple the 1 * 5 = 5 (the 5 side length in the diagram), then also multiple (5 * √3 = 5√3) and (2 * 5 = 10)

since you're looking for the hypotenuse (the length across the 90°), the answer would be 10 (2 * 5 = 10)

*this method can work for any 30° - 60° - 90° triangle

you can also use trig:

sin (30°) =
`(5)/(x)` (now just solve for x)

x * sin (30°) = 5

x =
`(5)/(sin(30))`

x =
`(5)/(1/2)` ( because sin (30°) = 1/2 )

x = 5 *
`(2)/(1)` = 10

*either method works!