Question

ii. Find RP and PS using the information given in APSR.
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Answer 1

Step-by-step explanation:

Here,

RS/RP= sin30°

6/RP= 1/2

6×2= RP

=12

and RS/PS= tan30°

6/PS= 1/√3

6√3= PS

6×1.732= 10.392

or after finding RP

RP²= PS²+RS²

12²= PS²+6²

PS= √144-36 = ✓108 = √2×2×3×3×3 = 6√3

Answer 2

Step-by-step explanation:

in ∆ PSR,

angle S = 90° and angle P = 30°

So, angle R = 60° ( remaining angle )

∆ PSR is a 30° - 60° - 90° triangle

by 30 ° - 60° - 90° triangle theorem,

RS = ½ × PR ( side opposite to 30° )

6 = ½ × PR

PR = 12 units.

PS = √3/2 × PR ( side opposite to 60° )

PS = √3/2 × 12

PS = 6√3 units.

That's your answer!