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Chapter 8: Q. 42 (page 535)

In the given problem solve the triangle using either the law of sines or law of cosines-

a=10,b=10,c=15

Short Answer

Expert verified

Required values of the triangle are

A=138.59掳,B=41.29掳,C=81.89掳

Step by step solution

01

Step 1. Given information

In the given triangle,

a=10,b=10,c=15

We know,

Law of cosines,

a2=b2+c2-2bccosA --------1

Law of sines,

sinAa=sinBb=sinCc ---------2

02

Step 2. Calculation

For A, using equation 1

role="math" localid="1646736804050" a2=b2+c2-2bccosA鈬�102=102-152-2脳10脳15cosA鈬�300cosA=-225鈬�cosA=-225300鈬�A=cos-1-0.75鈬�A=138.59掳

For Band C, using 2

sinAa=sinBb鈬�sin138.59掳10=sinB10鈬�sinB=0.66鈬�B=sin-10.66=41.29掳

Also,

sinBb=sinCc鈬�sin(41.29掳)10=sinC15鈬�sinC=0.6610脳15鈬�sinC=0.99鈬�C=sin-10.99=81.89

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