1) The problem says that the quilt squares are cut on the diagonal to form triangular quilt pieces. Then, the triangle pieces have angles of 45°, and the legs have the same lenght. So, you can solve the exercise by applying the Pythagorean Theorem:
 h²:s²+s²
 h²=2s²
 h²/2=s²
 s=√(h²/2)
 "h" is the hypotenuse (h=10 inches) and "s" is the length of the sides.
 When you substitute the value of the hypotenuse into the formula s=√(h²/2), you obtain the sides length:
 s=√(h²/2)
 s=√(10²/2)
 s=5√2
 What is the side length of each piece?Â
 The answer is: 5√2
 2)Tan(α)=Opposite/Adjacent
 α=30°
 Opposite=17
 Adjacent=x
 When you substitute these values into Tan(α)=Opposite/Adjacent, you obtain:
 Tan(α)=Opposite/Adjacent
 Tan(30°)=17/x
 x=17/Tan(30°)
 x=17√3
 Sin(α)=Opposite/Hypotenuse
 α=30°
 Opposite=17
 Hypotenuse=y
 Then, you have:
 Sin(30°)=17/y
 ySin(30°)=17
 y=17/Sin(30°)
 y=34
