Question

From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?

Answer 1

To find the height of the mat off the ground, we can use trigonometry.

Step-by-step explanation:

To find the height of the mat off the ground, we can use trigonometry. Since the angles of the right triangle formed by the mat are 60° and 30°, we can determine the height using the sine function. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.

In this case, the side opposite the 30° angle is the height of the mat, and the hypotenuse is the length of the mat, which is 5 feet. So, we have sin(30°) = height/5. Solving for the height, we get height = 5 * sin(30°) = 5 * 0.5 = 2.5 feet.

Therefore, the mat is 2.5 feet off the ground.