Question

Analyze the diagram below and complete the instructions to follow.

Find a, b and c

Answer 1

Answer/Step-by-step explanation:

✔️Using trigonometric ratio, find b:

Reference angle = 45

opposite = 8

Hypotenuse = b

Thus,

Sin(45) = 8/b

b = 8/sin(45)

b = 8/(1/√2) (sin 45 = 1/√2)

b = 8 × √2/1

b = 8√2

✔️Find a using trigonometric ratio:

Reference angle = 60°

Hypotenuse = b = 8√2

Adjacent = a

Therefore,

Cos(60) = a/8√2

8√2*cos(60) = a

8√2*½ = a

4√2 = a

a = 4√2

✔️Find c using Pythagorean Theorem:

c² = b² - a²

c² = (8√2)² - (4√2)²

c² = 128 - 32

c² = 96

c = √96

c = √(16*6)

c = 4√6