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
