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    Probs a really easy question but cant seem to get it! Plz help

    A chord AB of a circle, with centre O and radius 11.5cm has length 13cm and subtends an angle of &(theta) radians at O, as shown.

    a) show that & = 1.20, to 3 s.f

    cheers guys!

    so there's a triangle formed with AB, and two radii as its sides. You can split this into two right-angled triangles (perpendicular to the line AB). By Pythagoras, the height of both of these triangles is root (11.5^2 - 6.5^2) which is root 90. So the area of one of these triangles is 0.5 x base x height = 30.8322....
    Now the initial triangle (formed with the two radii and the line AB) has its area 0.5 x A x B x sin&.
    Taking the area of the big triangle as 2 x area of right-angled ones, it becomes (2 x 30.8322) = 0.5 x 11.5 x 11.5 x sin&
    so you can work out & as 1.2.
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Updated: April 12, 2006
“Yanny” or “Laurel”
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