Question

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

Answer 1

Answer:

A. a = √2

b = √2

Step-by-step explanation:

Apply trigonometric function to find a and b:

Reference angle = 45°

Hypotenuse = 2

Opposite side = a

Adjacent side = b

✔️Apply SOH to find a, which is:

Sin 45 = Opp/Hyp

Sin 45 = a/2

2*Sin 45 = a

2*1/√2 = a (sin 45 = 1√2)

2/√2 = a

Rationalize

(2*√2)/(√2*√2) = a

2√2/2 = a

√2 = a

a = √2

✔️Apply CAH to find b, which is:

Cos 45 = Adjacent/Hypotenuse

Cos 45 = b/2

2*Cos 45 = b

2*1/√2 = b (Cos 45 = 1√2)

2/√2 = b

Rationalize

2√2/2 = b

√2 = b

b = √2