Value of b is 11.25
Step-by-step explanation:
Step 1:
Use the trigonometric ratio sine to find z.
⇒ sin 60° = opposite side/hypotenuse = z/15
∴ z = 15 sin 60° = 15√3/2
Step 2:
Use the trigonometric ratio sine to find y.
⇒ sin 30° = opposite side/hypotenuse = y/z
∴ y = z sin 30° = 15√3/2 × 1/2 = 15√3/4
Step 3:
Use Pythagoras theorem to find value of b.
⇒ y² + b² = z²
⇒ b² = z² - y² = (15√3/2)² - (15√3/4)²
= (15 × 15 × 3/4) - (15 × 15 × 3/4²)
= 15²×3/4 [1 - 1/4] (taking common factor out)
= 15² × 3/4 × 3/4 = 15² × 3²/4²
∴ b = √15² × 3²/4² = 15 × 3/4
= 45/4 = 11.25
