Asked by Nick
find the area of a circle inscribed in triangle ABC where a=9, b=13, and the measure of angle C=38 degrees
Answers
Answered by
bobpursley
You can get c with the law of cosines.
Then, draw the figure. You have a multitude of similar triangles. The idea is to use them to find the measure of radius, the distance on many of those triangles.
Then, draw the figure. You have a multitude of similar triangles. The idea is to use them to find the measure of radius, the distance on many of those triangles.
Answered by
Nick
I've tried that multiple times, but I was told the answer should be more than one. I get something around .07
Answered by
Reiny
As suggested by bobpursley, use the cosine law to get c, I got 8.1
Now use the Sine Law to find angle A, which I got to be 43.16º
Let P be the centre of the incsribed triangle. A property of that circle is that its centre is the intersection of the angle bisectors of the triangle.
Consider triangle APC. Angle C is 19º, AC = 13 and angle A is 21.58º
(If you have a triangle with its base known and the two angles on that base A and C are known, then the height is given by
Height = base/(cot A + cot C)
in this case
height = 13/(cot19º + cot21.58º)
= 2.393
This is the radius of your circle, so the area is pi(2.393)^2
= 17.99 or 18 units
Now use the Sine Law to find angle A, which I got to be 43.16º
Let P be the centre of the incsribed triangle. A property of that circle is that its centre is the intersection of the angle bisectors of the triangle.
Consider triangle APC. Angle C is 19º, AC = 13 and angle A is 21.58º
(If you have a triangle with its base known and the two angles on that base A and C are known, then the height is given by
Height = base/(cot A + cot C)
in this case
height = 13/(cot19º + cot21.58º)
= 2.393
This is the radius of your circle, so the area is pi(2.393)^2
= 17.99 or 18 units
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