Question

http://gyazo.com/ecaceb89b3a014abf50e53dbeaebf4ef.png?1354481207

I can't get my head around this question. I've got that SR=PRtan35 and SR=QRtan40, which looks like it could help, but I can't figure it out. Please help? :)

Answer 1

let h = height of pole

sin(40) = h/QS

QS*sin(40) = h

QS = h/sin(40)



sin(35) = h/PS

PS*sin(35) = h

PS = h/sin(35)

Answer 2

each triangle PRS and QRS are right triangles so we can say


PR^2 + RS^2 = PS^2

PR^2 + h^2 = PS^2

PR^2 + h^2 = (h/sin(35))^2


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QR^2 + RS^2 = QS^2

QR^2 + h^2 = QS^2

QR^2 + h^2 = (h/sin(40))^2

Answer 3

Now use what you found

SR=PRtan35 and SR=QRtan40

PRtan35 = QRtan40

PR = QR*tan(40)/tan(35)

Answer 4

Since PR = QR*tan(40)/tan(35)

we go from

PR^2 + h^2 = (h/sin(35))^2

to

( QR*tan(40)/tan(35) )^2 + h^2 = (h/sin(35))^2

if you let x = QR and y = h, then we get this equation

( x*tan(40)/tan(35) )^2 + y^2 = (y/sin(35))^2

Answer 5

again, let x = QR and y = h

to go from

QR^2 + h^2 = (h/sin(40))^2

to

x^2 + y^2 = (y/sin(40))^2

Answer 6

so you now have these 2 equations (with 2 unknowns)

( x*tan(40)/tan(35) )^2 + y^2 = (y/sin(35))^2
x^2 + y^2 = (y/sin(40))^2