See adjoining figure. Find RP and PS using the information given in �

1.	See adjoining figure. Find RP and PS using the information given in ∆PSR.
Answer» In ∆PSR, ∠S = 90° , ∠P = 30° [Given] ∴ ∠R = 60° [Remaining angle of a triangle] ∴ ∆PSR is a 30° – 60° – 90° triangle. RS = 1/2 RP [Side opposite to 30°] ∴6 = 1/2 RP ∴ RP = 6 × 2 = 12 units Also, PS = \( {\sqrt{3} \over 2}\) RP [Side opposite to 60°] = \( {\sqrt{3} \over 2}\) × 12 = \( {6\sqrt{3} }\) units ∴ RP = 12 units, PS = \( {6\sqrt{3} }\) units

See adjoining figure. Find RP and PS using the information given in ∆PSR.

Answer»

In ∆PSR, ∠S = 90° , ∠P = 30° [Given]

∴ ∠R = 60° [Remaining angle of a triangle]

∴ ∆PSR is a 30° – 60° – 90° triangle.

RS = 1/2 RP [Side opposite to 30°]

∴6 = 1/2 RP

∴ RP = 6 × 2 = 12 units

Also, PS = \( {\sqrt{3} \over 2}\) RP [Side opposite to 60°]

= \( {\sqrt{3} \over 2}\) × 12

= \( {6\sqrt{3} }\) units

∴ RP = 12 units, PS = \( {6\sqrt{3} }\) units