I’m unsure of how to solve this type of problem and I’m not sure what to look up to find help, does anyone know?

Correct b = 1 and a = √2

Step-by-step explanation:

Given:

Right triangle

One leg with length 1 unit

One acute angle α = 45°

a, b = ?

The theorem says that two acute angles in a right triangle are complementary, ie their sum is 90 degrees.

α + β = 90°  ⇒ β = 90° - 45° = 45°

β = 45°   this means that the other angle is also 45 degrees

The theorem says that across the equal angles are equal sides.

Accordingly the other leg b is one unit  ⇒ b = 1

Finally, we apply Pythagoras' Theorem:

b² + 1² = a²

a² = 1 + 1 = 2  ⇒ a = √2

a = √2

God is with you!!!

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.