SOLUTION: Question: AT and BT are tangents to a circle, center O and radius 10cm. The length of the arc AB is 16cm. find (a)the size of angle AOB. (b)the area of triangle ABT. an image of

Algebra ->  Surface-area -> SOLUTION: Question: AT and BT are tangents to a circle, center O and radius 10cm. The length of the arc AB is 16cm. find (a)the size of angle AOB. (b)the area of triangle ABT. an image of       Log On


   

Question 828031: Question: AT and BT are tangents to a circle, center O and radius 10cm. The length of the arc AB is 16cm. find (a)the size of angle AOB. (b)the area of triangle ABT.
an image of the diagram i sketched
http://postimg.org/image/eyky5f98h/
i solved (a) and it was 1.6 radians, however i couldn't find a way to calculate the area of triangle ABT as the shape OATB is a Kite and we only have the radius, angle AOB and angles TAO=TBO=pi/2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
ABT is an isosceles triangle, with AT=BT.
You could calculate its area as %28AT%29%2A%28BT%29%2Asin%28ATB%29%2F2=%28AT%29%5E2%2Asin%28ATB%29%2F2
You need the measure of angle ATB, and the length of side AT.

Since you know 3 of the 4 angles in kite ATBO, you can easily calculate the measure of angle ATB, as
2pi-pi%2F2-pi%2F2-1.6=pi-1.6=1.5416 (rounded)

You can calculate AT from right triangle OAT.
Angle AOT is half of angle AOB, and
AT%2FAO=tan%28AOT%29 so AT=AT%2Atan%28AOT%29=%2810cm%29%2Atan%280.8%29=10.3cm

So the area of ABT is
%2810.3cm%29%5E2%2Asin%281.5416%29%2F2=53.0 (rounded).