Suppose a triangular desk will be built in the corner of that room. It will be in the shape of a 30-60-90 right triangle. The length of the longer leg of the triangle is 5 feet.

The volume of the room is 566 sq ft

2. How could the length of the shorter leg be determined without measuring it? What is its length? Round your answer to the second decimal point. Show all of your work.

3. How could the length of the hypotenuse be determined without measuring it? What is its length? Round your answer to the second decimal point. Show all of your work.

Longer leg = 5 feet

Shorter leg ≅ 2.89 feet

Hypotenuse ≅ 5.78 feet

Step-by-step explanation:

Let's recall that this is a special type of triangle where the three angles measure 30 degrees, 60 degrees, and 90 degrees. The ratio of the sides is 1:  √3  :2. That is to say, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of 3 times the shorter leg.

Upon saying that, we can find the length of the legs of the triangle given:

Longer leg = 5 feet

Shorter leg * √3 = 5

Shorter leg = 5/√3 = 5√3/3 ≅ 2.89 feet

Hypotenuse = 2 * Shorter leg

Hypotenuse = 10√3/3 ≅ 5.78 feet

a. she will receive a refund of $278.

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