HSC Arts 12th Board ExamMaharashtra State Board
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The angles of the ΔABC are in A.P. and b:c=sqrt3:sqrt2 then find ∠A, ∠B, ∠C - HSC Arts 12th Board Exam - Mathematics and Statistics

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Question

The angles of the ΔABC are in A.P. and b:c=`sqrt3:sqrt2` then find`angleA,angleB,angleC`

 

Solution

`angleA, angleB, angleC` are in A.P and `b:c=sqrt3:sqrt2`

`therefore 2B=A+C`

`2B=180^@-B`     ...............[`because A+B+C=180^@`]

`3B=180^@`

`angleB=60^@`

In ΔABC by sine rule, we have

`sinB/b=sinC/c`

`sinB/sinC=b/c`

`sin60^@/sinc=sqrt3/sqrt2`

`sqrt3/2=sqrt3/sqrt2=sinC`

`sinC=1/sqrt2`

`angle C=45^@`

`angleA=180^@-60^@-45^@=75^@`

Thus, the angles of ΔABC are `angleA=75^@,angleB=60^@,angleC=45^@`

 

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APPEARS IN

 2016-2017 (July) (with solutions)
Question 2.2.3 | 4.00 marks
Solution The angles of the ΔABC are in A.P. and b:c=sqrt3:sqrt2 then find ∠A, ∠B, ∠C Concept: Trigonometric Functions - Solution of a Triangle.
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