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If the sides of a triangle are in A.P. ...

If the sides of a triangle are in A.P. and the greatest angle of the triangle exceeds the least by `90^(@)`, then sine of the third angle is

A

`(sqrt5)/4`

B

`(sqrt6)/4`

C

`(sqrt7)/4`

D

none of these

Text Solution

Verified by Experts

Let ABC be a triangle with the greatest and least angles as A and C respectively. Then,
`A-C=90^(@)` [Given]
lt is given that a, b, c are in A.P.
`therefore2b=a+c`
`rArr2sinB=sinA+sinC`
`rArr2sinB/2cosB/2=sin(A+C)/2cos(A-C)/2`
`rArr2sinB/2=cospi/4rArrsinB/2=1/(2sqrt2)`
`thereforesinB=2sinB/2cosB/2=2xx1/(2sqrt2)xx(sqrt7)/(2sqrt2)=(sqrt7)/4`
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