Question

A billiard ball is struck by a cue. It travels 100 cm before ricocheting off a rail and traveling another 100 cm into a corner pocket. The angle between the path as the ball approaches the rail and the path after it strikes the rail is 45 degrees. How far is the corner pocket from where the cue initially struck the ball?

Answer 1

Answer:

76.53 cm

Step-by-step explanation:

From the question, the triangle formed has 2 sides and an included angle ;

Angle, θ = C = 45°

We use cosine rule :

Taking the side to find as c

a = 100 ; b = 100

From cosine rule :

c = sqrt(a² + b² - 2abCosC)

c = sqrt(100² + 100² - 2(100*100)Cos45

c = sqrt(10000 + 10000 - 20000 * 0.7071067)

c = sqrt(20000 - 14142.135)

c = sqrt(5857.865)

c = 76.536690

c = 76.53 cm