Question #11a8a

2 Answers
Apr 18, 2017

The Law of Cosines states that, for a triangle with sides a,b, and c with the angle C opposite side c, that:

c^2=a^2+b^2-2abcos(C)

Angle C is opposite side c=bar(AB)=8. We also see that side a=bar(BC)=12 and b=bar(CA)=15. Plugging these into the Law gives:

8^2=12^2+15^2-2(12)(15)cos(C)

64=144+225-360cos(C)

-305=-360cos(C)

cos(C)=305/360=61/72

Solving for C:

C=cos^-1(61/72)=32˚

Apr 18, 2017

32°

Explanation:

From the figure a=12cm, b=15cm, c=8cm

Now just apply the formula,

cosC= (a^2 +b^2-c^2)/(2ab)

cosC=(305/360)

cosC=(61/72)

61/72 is close to sqrt3/2

So C=cos^-1(61/72) approx 30^@

You get angle C as 32°.