If the angles of a triangle are in the ratio 2 : 3 : 7 ,then the sides are in the ratio

Options

A. `sqrt2 :2:sqrt3 + 1`
B. `2:sqrt2:sqrt3:1`
C. `sqrt2:sqrt3+1:2`
D. `2:3:7`

Answer

A

Explanation

Let ABC be triangle whose angles A, B and C are in the ratio 2 : 3 : 7.
Let A = 2`lamda, B == 3lamda` and C = `7lamda` . Then,
A + B + C = 180° `rArrlamda = 15`
`therefore` A=30°, B=45° and C =105°
`therefore a/(sinA)=b/(sinB)=c/(sinC)`
`rArra/(sin30^(@))=b/(sin45^(@))=c/(sin105^(@))`
`rArra/(1/2)=b/(1/(sqrt2))=c/((sqrt3+1)/(2sqrt2))rArra/(sqrt2)=b/2=c/(sqrt3+1)`