Calculate

[silver nymph]

(a) length of PS
(b) length of PR and QR
(c) Area △PQS

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[wind fox]

can you find distance from point R to line PQ, that will be the base of right isosceles triangle with a hypotenuse of PS

[silver nymph]

I did but getting a wrong answer .

[wind fox]

what did you do

[silver nymph]

I first calculated the distance with Sin and then applied cos to find PS .

[wind fox]

sin of what

[silver nymph]

sin 60

sin Q

[wind fox]

and that gives you PR?

[silver nymph]

yes

[wind fox]

so then did you do another trig function to find the distance from R to PQ

[silver nymph]

can you elaborate? I am new to trigonometry

[wind fox]

so
lets call the point east of P on QR as T
then, <QPR = 30°, so <TPR = 60°
you would like to know PT
and you have PR

[silver nymph]

oh ok so PT should be 40 ? ( using the sin law)

[wind fox]

what sin law are you using

[silver nymph]

sin a / a = sin b / b

[wind fox]

i don't know what triangle you're talking about

but no

what value of PR did you get

[silver nymph]

34.64

[wind fox]

this is correct

now what is <TPR

[silver nymph]

60

[wind fox]

so what's PT/PR

[silver nymph]

cant solve it :/

[wind fox]

ok
PT/PR is sin(<TPR)
so PT = PRsin(<TPR)
sin(60) = 1/2
PT = PR/2 = 17.32

[silver nymph]

yes thank you it is giving the right answer but we have to find PS first then PR according to the order ? How we will find PS without finding PR first?

[wind fox]

what? you already found PR

you don't have to find the things it asks for in the order it asks for them

[little perch]

@silver nymph has given 1 rep to @wind fox

[silver nymph]

oh ok thank you sir .

[wind fox]

no problem

[silver nymph]

if you dont mind ; can you help in finding the area of the PQS?

[wind fox]

the base is PQ, then the height is the very same distance we were finding before
so PQS has the same area as PQR

[silver nymph]

it is giving me 346.4 but answer is 364.4

[wind fox]

i think the answer is 346.4

[silver nymph]

I've checked it ; it is 364.4 . I would confirm from the instructor thank you again.

[wind fox]

i believe the instructor made an error