3. Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles. Is 18 inches long. What is the side length of each piece? 4. Find the missing value to the nearest hundredth. sin________=8/15

These are two questions and two answers:

Question 3.

Answer: fourth option 9√2

Explanation:

1) Since the original quilt is square, you know that the diagonal length is the hypotenuse of the two triangles formed and it satifies this formula, derived from the Pythagorean theorem:

(diagonal) ^2 = (hypotenuse)^2 = 2 * (side length)^2

2) Solve for the side length:

(side length)^2 = (diagonal)^2 / 2

=> side length = √ [ (diagonal)^2 / 2 ] = diagonal * (√2) / 2

3) Substitute the diagonal length value:

side length = 18 * (√2) / 2 = 9√2

Question 4

Answer: second option 32.23°

Explanation

1) Given sin(angle) = 8 /15

2) To find the angle you have to use the inverse function, arcsin

angle =  arcsin (8/15)

3) The calculator uses that function and the result that it gives is 32.23°.

To avoid confusions make sure that the calculator is in mode degrees.