SOLUTION: Triangle ABC is right angled at B. If AB = 15 cm and BC = 20 cm, what is the area of circle centered at B and tangent to the hypotenuse AC.

Algebra ->  Triangles -> SOLUTION: Triangle ABC is right angled at B. If AB = 15 cm and BC = 20 cm, what is the area of circle centered at B and tangent to the hypotenuse AC.       Log On


   

Question 935044: Triangle ABC is right angled at B. If AB = 15 cm and BC = 20 cm, what is the area of circle centered at B and tangent to the hypotenuse AC.
Answer by lwsshak3(11628) About Me  (Show Source):
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Triangle ABC is right angled at B. If AB = 15 cm and BC = 20 cm, what is the area of circle centered at B and tangent to the hypotenuse AC.
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In the right triangle described above, label the point of tangency O.
r=radius of circle=BO
tanC=15/20=3/4=0.75
C≈36.87˚
Using right riangle BOC:
sinC=BO/20
BO=20sinC=20sin36.87˚=12
Area of circle=πr^2=π(12^2)=144π cm^2