Answer:
a = 4
b = 2√2
Step-by-step explanation:
First, we will calculate the sine of 45°, which is equal to the length of the opposite side (2√2) divided by the length of the hypotenuse (a).
sin 45° = 2√2 / a
a = 2√2 / sin 45°
We know than sin 45° = √2/2
a = (2√2) / (√2/2) = 4
Then, we calculate the tangent of 45°, which is equal to the length of the opposite side (2√2) divided by the length of the adjacent side (b).
tan 45° = 2√2 / b
b = 2√2 / tan 45°
We know that tan 45° = 1
b = 2√2 / 1 = 2√2
