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.
