•• quilt squares are cut on the diagonal to form triangular quilt pieces the hypotenuse of the resulting triangle is 10 inches long what is the side length of each piece?

-5
-5√2
-5√3
-10√2

•• find the length of the missing sides in the triangle a triangle is not drawn to scale.

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? 

 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