Question

PLEASE HELP!!!!!
Given that RS=18 and QR=6, identify the length of PS

Answer 1

12√3

Explanation:

cos∠RSP = 18/PS

cos∠PSQ = PS/24

∠RSP=∠PSQ (the angle at S)

18/PS = PS/24

(PS)² = (18)(24) = 432

PS = √432 = 12√3

Answer 2

12 root 3

Explanation:

first, you can say that QRP is similar to PRS

with the ratios, you can say that

`(QR)/(PR) = (PR)/(RS)\\`

by substituting values, you have

`(6)/(PR) = (PR)/(18)\\`

`PR^2=108`

`PR=6√(3)`

using pythagorean theorem, you can determine that

`PS^2=(6√(3))^2+18^2`

`PS^2=432`

`PS=√(432)=12√(3)`