You can use this webpage.
There is a question on the area of a sector of a circle on which I am stuck and was wondering whether anyone could give me a pointer.
I have attached an image of the diagram to which the question refers...
The diagram shows an arc of ABC of a circle centre o and radius 10cm.
Angle AOB = radians and angle AOC is a right angle.
a. Write down, in terms of theta, the area of sector AOB.
I can do this easily enough:
b. Show that the area of the shaded segment is
This is where I get stuck.
I can find the area of the sector OBC using the formula and get
But I can't see how to get the area of the triangle.
Having said that, multiplying out gives:
, so the area of the triangle must be .
I just can't see how to get at this area for the triangle, though. Any advice would be greatly appreciated!
That's a isosceles triangle having two sides of length 10 and one angle of measure . If you drop a perpendicular, you divide it into two right triangles having hypotenuse 10 and angle . So the two legs of the right triangle have length and . Since the legs are the "base" and "altitude" of a right triangle, the area of each is and the area of the entire triangle is .
Thank you for your replies. Plato, thanks for the link; it looks interesting but involves cotangents which I have not yet got to in my mathematical education.
Thanks for your explanation Halls of Ivy. I can follow your working but there is just one thing I don't understand (I am probably failing to see something obvious):
How do you know one of the angles in the isocoles triangle is ? The only conclusion I could draw was that the angle would be radians.
Thanks again for your help.