The shortest side of a right triangle measures 3 squared 3
inches. One angle of the triangle measures 60 degrees
. What is the length, in inches, of the hypotenuse of the triangle?
In a right triangle, the side opposite the right angle is called the hypotenuse.
We are given that one angle of the triangle measures 60 degrees. In a right triangle, one of the angles measures 90 degrees. Therefore, the remaining angle measures 180 degrees - 90 degrees - 60 degrees = 30 degrees.
We are also given that the shortest side of the triangle measures 3 sqrt(3) inches. This side will be opposite the 30 degree angle.
Using the trigonometric ratios for a 30-60-90 triangle, we can determine the length of the hypotenuse.
In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows:
- The length of the side opposite the 30 degree angle is 1.
- The length of the side opposite the 60 degree angle is sqrt(3).
- The length of the hypotenuse is 2.
Since we are given that the shortest side of the triangle measures 3 sqrt(3) inches, we can write the following equation:
(sqrt(3)) / (3 sqrt(3)) = 1 / x
Cross-multiplying, we get:
1 * (3 sqrt(3)) = (sqrt(3)) * x
3 sqrt(3) = sqrt(3) * x
Simplifying, we have:
3 = x
Therefore, the length of the hypotenuse is x = 3 inches.