MathRevolution wrote:
Attachment:
Triangle ABC.jpg
If the triangle ABC is inscribed in semi-circle BAC as above figure and BC is a diameter, the length of AB is 6 and the length of AC is 8, what is the length of arc BAC?
A. 5π(pi)
B. 6π(pi)
C. 7π(pi)
D. 8π(pi)
E. 10 π(pi)
Since BC is the diameter of the semi-circle, we know that ∠BAC is 90º
In other words, we can conclude that BAC is a RIGHT TRIANGLE and side BC is the HYPOTENUSE.
This means we can apply the Pythagorean Theorem to get: 6² + 8² = (side BC)²
Simplify: 36 + 64 = (side BC)²
Simplify: 100 = (side BC)²
So, side BC = 10
In other words, the DIAMETER =
10Circumference of COMPLETE circle = (DIAMETER)(π)
So, circumference of SEMIcircle = (DIAMETER)(π)/2
= (
10)(π)/2
= 5π
= A
Cheers,
Brent
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