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

ConceptTrigonometric Functions Solution of a Triangle

Question

The angles of the ΔABC are in A.P. and b:c=sqrt3:sqrt2 then findangleA,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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