anonymous
  • anonymous
In the diagram, OPQ is a sector of a circle, centre O and radius r cm. Angle QOP = Theta radians. The tangent to the circle at Q meets OP extended at R. (i) Show that area, A cm^2, of the shaded region is given by A=(r^2/2)(tan theta- theta). (ii) In the case where theta=0.8 and r= 15, evaluate the length of the perimeter of the shaded region.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1332837582282:dw|
anonymous
  • anonymous
Sorry, my circle's wonky...
anonymous
  • anonymous
@dpaInc

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More answers

anonymous
  • anonymous
|dw:1332837898353:dw|
anonymous
  • anonymous
|dw:1332838221910:dw| Area of shaded region = A[triangle] - A[sector]
anonymous
  • anonymous
i'm just jotting things down...
anonymous
  • anonymous
Isn't tan Opposite/hypotenuse?
anonymous
  • anonymous
tan is opp/adjacent
anonymous
  • anonymous
Oh, OK
anonymous
  • anonymous
tan(theta) = h/r so h=r*tan(theta)
anonymous
  • anonymous
|dw:1332838594184:dw|
anonymous
  • anonymous
|dw:1332838696361:dw|
anonymous
  • anonymous
is that the first one?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
ok, for the second one...|dw:1332838826550:dw|
anonymous
  • anonymous
perimeter = s + QR + PR
anonymous
  • anonymous
Wait, what's the length of the arc?
anonymous
  • anonymous
it's s = r*theta. remember, in all these formulas, theta is in radians...
anonymous
  • anonymous
So, how do you get PR and QR?
anonymous
  • anonymous
|dw:1332839082189:dw|
anonymous
  • anonymous
you ca get QR and PR by solving whats in the circled part...|dw:1332839209401:dw|
anonymous
  • anonymous
to get OR, you can solve the equation: cos(.8) = 15/OR so OR = 15/cos(.8)
anonymous
  • anonymous
I got a weird answer for QR.
anonymous
  • anonymous
No, I didn't get that. Hold on
anonymous
  • anonymous
QR = 15.44
anonymous
  • anonymous
Yes, I got it now :)
anonymous
  • anonymous
you got PR?
anonymous
  • anonymous
Yes, 6.52986...
anonymous
  • anonymous
good. s should be a piece of cake. add them all up to get your perimeter.
anonymous
  • anonymous
s=12?
anonymous
  • anonymous
yep.
anonymous
  • anonymous
Thanks :)
anonymous
  • anonymous
anytime... and good work.

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