Answer:
Step-by-step explanation:
the smaller triangle on the left is a 45-45-90. That means that sides a and c are the same length. The Pythagorean triple for a 45-45-90 is (x, x, x√2) where x is the length across from both the 45 degree angles, and x√2 is the side length across from the right angle (which is also the hypotenuse). If the hypotenuse measures 2√2 and the formula for this side length is x√2, then
x√2 = 2√2 making
x = 2.
Therefore, a = c = 2.
Now, for the other triangle on the right, which is a 30-60-90. The Pythagorean triple for this triangle is (x, x√3, 2x), where x is the length of the side across from the 30 degree angle, x√3 is the length of the side across from the 60 degree angle, and 2x is the length of the hypotenuse. If the side across from the 30 degree angle measures 2, then d, being the side across from the 60 degree angle measures 2√3 (d = 2√3) and the hypotenuse, side b, measures 4. To sum it all up:
a = 2
b = 4
c = 2
