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?

The mat is 4.33 ft high off the ground.

Step-by-step explanation:

Since we have given that

Angle of elevation with the first triangle = 30°

Angle of elevation with the second triangle = 60°

Length at which gymnastics mat extends across the floor = 5 feet

so, As shown in the figure:

We need to find the height of the mat off the ground.

If CD = 5 ft,

Let,  AB = y, DC = x.

In Δ ABC,

Similarly, in Δ ACD,

Hence, the mat is 4.33 ft high off the ground.

Answer with explanation:

Description of gymnastic mat

Two interior angles of mat which is in the shape of right triangle are 60° and 30°.

Let the base and height of mat are x feet and y feet and Hypotenuse be z feet.

Now, when mat extends 5 feet across the floor,angle of inclination will decrease that is will be less than 30° but the triangle will be a right triangle.

Length of base =(√3 y +5) Feet

Length of Hypotenuse = H feet> z>2 y

The height of gymnastic mat before and after extension will be same.

→→There is another possibility also.

If the total extension of the mat is 5 feet,then

Length of base of mat =5 feet

Height of mat =2.89 feet(Approx)

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3