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Chapter 8: Q.20 (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�c=5,b=4,A=70

Short Answer

Expert verified

The remaining sides and angles area=5.22B=46C=64

Step by step solution

01

Step 1.  Given information    

The given data isc=5,b=4,A=70

02

Step 2. Find the length of side a

Use the cosines rule of Law,cosA=b2+c2-a22bc

Here, c=5,b=4,A=70

cosA=b2+c2-a22bccos70=42+52-a22*4*50.34=16+25-a2400.34*40=41-a2a2=41-13.68a2=27.32a=5.22

03

Step 3.Find the angle B

Use the Law of Sines sinAa=SinBb=SinCc

Here,A=70,a=5.22,b=4,c=5

sinAa=SinBb=SinCcsin705.22=SinB4SinB=4sin705.22SinB=0.72B=46

04

Step 4. Find the angle C

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

A+B+C=18070+46+C=180C=180-116C=64

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