Find the length of x and y in the 30°-60°-90° triangle. Leave answer in simplest radical form.
show work.
The ratios of the sides of a 30-60-90 triangle are:
- The side opposite the 30-degree angle is x.
- The side opposite the 60-degree angle is x * sqrt(3), or y.
- The hypotenuse, opposite the 90-degree angle, is 2x.
We are given that the hypotenuse is 10. So, 2x = 10. Solving for x, we have x = 5.
Now we can find the length of y. y = x * sqrt(3) = 5 * sqrt(3).
Therefore, the lengths of x and y are x = 5 and y = 5 * sqrt(3).