Question

Find the value of each variable.

x = ???
y = ???

simplify your answers. type exact answers, using radicals as needed.

Answer 1

x = 6 y = 6√3

Step-by-step explanation: x = 6 is found sin(30) * 12

y =6√3 = 10.39230485 is found sin(60) * 12 because both x and y = sin x (opp/hyp)

Answer 2

x = 6 and y = 6
`√(3)`

Explanation:

Remember: In a 30°- 60°- 90° triangle the hypotenuse = short leg · 2

and the long leg = short leg ·
`√(3)` .

In the given right triangle you have the following opposite the right angle is the hypotenuse = 12, the long leg is opposite the 60° angle = y, and the short leg is opposite the 30° angle = x

1. Find the short leg "x"

Using hypotenuse = short leg · 2

12 = x · 2

12/2 = x

6 = x the short leg is 6

2. Find the long leg

Using long leg = short leg ·
`√(3)`

y = 6
`√(3)`