In triangle ABC, ∠B = 90° and tan A = 0.75. If AC = 30 cm, find the lengths of AB and BC.

Given: tan A = 0.75 = tan A = ∴ If length of AB = 4x unit, length of BC = 3x unit. In Δ ABC, ⇒ AC2 = AB2 \+ BC2 (∵ AC is hypotenuse) ⇒ AC2 = (4x)2 \+ (3x)2 ⇒ AC2 = 16x2 \+ 9x2 ⇒ AC2 = 25x2 ⇒ AC = ⇒ AC = 5x It is given that AC = 30 cm. So, 5x = 30 x = Therefore, AB = 4x = 4 x 6 cm = 24 cm and BC = 3x = 3 x 6 cm = 18 cm. Hence, AB = 24 cm and BC = 18 cm.