Question

In the figure given below, find RS and PS using the information given in ΔPSR.

Answer 1

∠P = 30°, ∠S = 90° and PR = 12

∠P + ∠S + ∠R = 180°  ...(Sum of measure of all angles of a triangle is 180°)

30° + 90° + ∠R = 180°

120° + ∠R = 180°

∠R = 180° − 120°

∠R = 60°

∴ By 30°-60°-90° theorem,

RS = `1/2 xx PR`  ...(Side opposite to 30°)

RS = `1/2 xx 12`

∴ RS = 6 units

PS = `sqrt3/2 xx PR`  ...(Side opposite to 60°)

PS = `sqrt3/2 xx 12`

PS = `6sqrt3` units