Question

if A=-35 then b= _ c= -5 verify that a /(b/c)=(a/b)/c=​

Answer 1

Step-by-step explanation:

MATHS

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Asked on December 27, 2019 by

Sankash Chavan

If in a △ABC,a

2

+b

2

+c

2

=8R

2

, where R= circumradius,then the triangle is

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ANSWER

Since, a

2

+b

2

+c

2

=8R

2

Using sine rule, we have

(2RsinA)

2

+(2RsinB)

2

+(2RsinC)

2

=8R

2

⇒4R

2

[(sinA)

2

+(sinB)

2

+(sinC)

2

]=8R

2

⇒sin

2

A+sin

2

B+sin

2

C=2

⇒1−cos

2

A+sin

2

B+1−cos

2

C=2

⇒−cos

2

A+sin

2

B−cos

2

C=2−2=0

⇒cos

2

A−sin

2

B+cos

2

C=0

⇒cos(A+B)cos(A−B)+cos

2

C=0

Since, A+B+C=π⇒A+B=π−C

⇒cos(π−C)cos(A−B)+cos

2

C=0

⇒−cosCcos(A−B)+cos

2

C=0

⇒cosC[−cos(A−B)+cosC]=0

⇒cosC=0,−cos(A−B)+cosC=0

⇒C=

2

π

or −cos(A−B)+cos(π−(A+B))=0

⇒−cos(A−B)−cos(A+B)=0

Using transformation angle formula, we have

⇒2cosAcosB=0

∴cosA=0,cosB=0

Hence ∠A=

2

π

or ∠B=

2

π

, or ∠C=

2

π