Find the value of x.

Question

A 30, 60, 90 degree right triangle is drawn. The 60 degree angle is labeled. The shortest leg adjacent to the 60 degree angle is labeled 5. The longest leg opposite the 60 degree angle is labeled y. The hypotenuse is labeled x.

5 times the square root of 3.
10
5 times the square root of 2.
5

Answer 1

In a 30-60-90 triangle, the relationships between the lengths of the sides are as follows:

• The side opposite the 30-degree angle (the shorter leg) is \( x \).
• The side opposite the 60-degree angle (the longer leg) is \( x \sqrt{3} \).
• The hypotenuse is \( 2x \).

From the problem, the shortest leg adjacent to the 60-degree angle (which is the leg opposite the 30-degree angle) is given as 5. Therefore, we can denote it as: \[ x = 5 \] The longer leg adjacent to the 60-degree angle can be calculated as: \[ y = x \sqrt{3} = 5 \sqrt{3} \] The hypotenuse can be calculated as: \[ \text{Hypotenuse} = 2x = 2(5) = 10 \]

Thus, the value of \( x \), which represents the hypotenuse, is: \[ \boxed{10} \]