Answer:
x = 24/√3
4√3 = y
Step-by-step explanation:
We are given that this is a right triangle as well as two angles and a side.
Given that the angles in a triangle add up to 180 degrees, and a right angle is 90 degrees, we can say that the missing angle is equal to
(180-90-30) = 60 degrees
Next, given sohcahtoa, we can say that
sin(30) = opposite/hypotenuse = y/x
cos(30) = adjacent/hypotenuse = 12/x
tan(30) = opposite/adjacent = y/12
We want to only have one variable per equation so we can solve for the variable, so we can use
cos(30) = 12/x and tan(30) = y/12
Starting with cos(30) = 12/x, we can multiply both sides by x to remove the denominator to get
cos(30) * x = 12, and divide both sides by cos(30) to isolate the x and get
x = 12/cos(30). Next, cos(30) = √3/2, so we have
x = 12/(√3/2)
x = (12/1) / (√3/2)
x = (12/1) * (2/√3)
x = 24/√3
For y, we have
tan(30) = y/12
multiply both sides by 12 to isolate the y and remove the denominator
tan(30) * 12 = y
√3/3 * 12 = y
√3 * 4 = y
4√3 = y
