Question

Find the missing side lengths and leave your answers as radicals in the simplest form.

Answer 1

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

Answer 2

Right triangle 45 45 90
so b = 2√2

and
a^2 = (2√2)^2 +  (2√2)^2
a^2 = 8 + 8 
a^2 = 16
a = 4