Question

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?

Answer 1

`y = 10 and x = 5sqrt3`

Explanation:

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

• the Pythagorean theorem,
• The trigonometric ratio: soh-cah-toa, and
• special values of trigonometric functions.

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

`sin30° =5/y`

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`