How do you find the value of X and Y. Y is the hypotenuse, 5 is the adjacent side and X is the opposite side from Y, and in the triangle there is 30 degrees where X and Y lines meet?

1 Answer
Oct 21, 2016

#y = 10 and x = 5sqrt3#

Explanation:

To find the values of x and y, you will need to use

enter image source here

Let's find the length of #y# first. Using SOH-CAH-TOA, we find that :

#sin30° =5/y#

enter image source here

Using the table of trig values, we find that #sin30° = 1/2#

So, this gives us:

#1/2 = sin30° = 5/y#

#1/2 = 5/y#

#(1xxy)/2 = 5#

# y = 2xx5 = 10#

Next, using the Pythagorean Theorem, we find that

#5^2 + x^2 = 10^2#

#x^2 = 100-25 = 75#

Solve for x:

#x = sqrt75 = sqrt(3xx25) = 5sqrt3#