In `DeltaABC`, if `sin A + sin B + sin C= 1 + sqrt2 and cos A+cos B+cosC =sqrt2` then the triangle is

Options

A. equilateral
B. isosceles
C. right angled
D. right angle isosceles

Answer

D

Explanation

If the triangle is equilateral
`sin A+ sin B+sin C=(3sqrt(3))/(2)`
If the triangle isosceles, let
`A=30^(@),B=30^(@), C=120^(@)`. Then,
`sin A+ sin B+ sin C=1+(sqrt(3))/(2)`
If the triangle is right angled, let
`A=90^(@), B=30^(@),C=60^(@)`. Then
`sin A+ sin B + sin C=(3+sqrt(3))/(2)`
If the triangle is right angled isoceles, then one of the angles is `90^(@)` and the remaining two are `45^(@)` each, so that
`sin A+ sin B + sin C = 1+sqrt(2)`
and `cos A + cos B + cos C = sqrt(2)`