Answer:
Correct answer: 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
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