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Chapter 8: Q.14 (page 553)

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say 鈥淣o triangle.鈥� a=10,b=7,c=8

Short Answer

Expert verified

The value of the remaining angles areA=83.3B=44C=52.7

Step by step solution

01

Step 1.  Given information     

The given data is a=10,b=7,c=8

02

Step 2. Find the angle A  

Use cosines Rule cosA=b2+c2-a22bc

Here, a=10,b=7,c=8

cosA=b2+c2-a22bccosA=72+82-1022*7*8cosA=49+64-100112cosA=13112A=83.3

03

Step 3. Find the angle B 

Use the Law of sines,sinAa=SinBb=SinCc

Here, A=83.3,a=10,b=7

sinAa=SinBb=SinCcsin83.310=SinB7SinB=7sin83.310SinB=0.69B=44

04

Step 4. Find the angle C 

Since the angle A, B, and c are the angel of a triangle,

A+B+C=18083.3+44+C=180C=180-127.3C=52.7

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