SOLUTION: The area of a circle is 5 pi and an arc 3 cm long cuts off a sector with an angle of theta subtended at the centre. Find theta

Algebra ->  Trigonometry-basics -> SOLUTION: The area of a circle is 5 pi and an arc 3 cm long cuts off a sector with an angle of theta subtended at the centre. Find theta      Log On


   

Question 1140826: The area of a circle is 5 pi and an arc 3 cm long cuts off a sector with an angle of theta subtended at the centre. Find theta
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A+=+pi%2Ar%5E2+
+pi%2Ar%5E2+=+pi%2A5+
+r%5E2+=+5+
+r+=+sqrt%285%29+
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Find the circumference:
+C+=+2%2Api%2Ar+
+C+=+2%2Asqrt%285%29%2Api+
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+3%2F%28+2%2Asqrt%285%29%2Api+%29+=+theta+%2F+%28+2%2Api+%29+
+theta+=+3%2Fsqrt%285%29+
+theta+=+1.3416+ radians
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In degrees:
+theta+%2F+%28+2%2Api+%29+=+1.3416+%2F+6.2832+
+%28+1.3416+%2F+6.2832+%29%2A360+=+.2135%2A360+
+.2135%2A360+=+76.8678+ degrees
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check the math and get a 2nd opinion if needed