Let's call the unlabeled side of the large triangle " x ".
And let's call the height of that triangle " h ".
By Pythagorean theorem, we can make the equation
x2 + y2 = (16 + 4)2
Subtract y2 from both sides of the equation.
x2 = (16 + 4)2 - y2
Again by the Pythagorean theorem, we can make the equation
162 + h2 = x2
Subtract 162 from both sides of the equation.
h2 = x2 - 162
Substitute (16 + 4)2 - y2 in for x2
h2 = (16 + 4)2 - y2 - 162
Again by the Pythagorean theorem, we can make the equation
42 + h2 = y2 Substitute (16 + 4)2 - y2 - 162 in for h2
42 + (16 + 4)2 - y2 - 162 = y2 Now we can solve for y .
Simplify the left side of the equation.
42 + 202 - y2 - 162 = y2
16 + 400 - y2 - 256 = y2
160 - y2 = y2
Add y2 to both sides of the equation.
160 = 2y2
Divide both sides by 2
80 = y2
Take the positive square root of both sides.
√80 = y
y = √[2*2 * 2*2 * 5]
y = 4√5