Question

One angle measures 30 degrees and another angle measures 60 degrees. The last angle of the right triangle is 90 degrees. The side opposite from the 60 degree angle is x. The side opposite of the 30 degree angle is y. The hypotenuse is 10. Find x and y

X=5, y= 5 square root 3
X=5. Y= 2
X=2 square root 3, y=10
X=5 square 3, y= 5

Answer 1

In a 30-60-90 triangle, the sides have specific ratios. The length of the side opposite the 30-degree angle is half the length of the hypotenuse, while the length of the side opposite the 60-degree angle is \( \sqrt{3} \) times the length of the side opposite the 30-degree angle.

Let’s denote:
- The side opposite the 30-degree angle as \( y \).
- The side opposite the 60-degree angle as \( x \).
- The hypotenuse as \( h \).

Given:
- The hypotenuse \( h = 10 \).

Using the properties of a 30-60-90 triangle:
1. \( y = \frac{1}{2}h \)
2. \( x = \frac{\sqrt{3}}{2}h \)

Now, calculate \( y \) and \( x \):

1. Find \( y \):
\[
y = \frac{1}{2} \times 10 = 5
\]

2. Find \( x \):
\[
x = \frac{\sqrt{3}}{2} \times 10 = 5\sqrt{3}
\]

So, the values are:
- \( x = 5\sqrt{3} \)
- \( y = 5 \)

Thus, the correct answer is:
**X = 5√3, Y = 5**.