Find part "b".

=_4_

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

sup

step-by-step explanation: