Consider a 30-60-90 triangle. The sides of a 30-60-90 triangle have a characteristic ratio of 1 : [tex]\( \sqrt{3} \)[/tex] : 2.
Let's break down the problem step-by-step:
1. Identify the sides of the triangle:
- Let [tex]\( a \)[/tex] represent the length of the shorter leg, which is the side opposite the 30° angle.
- The side opposite the 60° angle is [tex]\( a \sqrt{3} \)[/tex].
- The hypotenuse, or the side opposite the 90° angle, is [tex]\( 2a \)[/tex].
2. Substitute the known length of the shorter leg:
We assume the length of the shorter leg [tex]\( a \)[/tex] is 1.
3. Calculate the sides using the ratios:
- The side opposite the 60° angle is [tex]\( 1 \times \sqrt{3} = \sqrt{3} \)[/tex].
- The hypotenuse is [tex]\( 2 \times 1 = 2 \)[/tex].
Thus, using these steps, we find:
[tex]\[
x = 1 \sqrt{3}
\][/tex]
[tex]\[
y = 2
\][/tex]
Hence, the values are:
[tex]\[
x=\sqrt{3}
\][/tex]
[tex]\[
y=2
\][/tex]
