Let `alpha, beta` are the root of equation `acostheta + bsintheta = c`.
If `alpha = 30^(@)` and `beta = 60^(@)` such that `a, b, c` represent sides of a `DeltaABC` then

Options

A. `ABC` is acute angle triangle
B. `ABC` is acute isosceles triangle
C. `ABC` is right angle triangle
D. `ABC` is obtuse angle triangle

Answer

A, B

Explanation

`alpha = 30^(@)` and `beta = 60^(@) rArr (a)/(2) = (b)/(2) = (c)/(sqrt(3) + 1)`
`rArr cosC = (2 - sqrt(3))/(4) gt 0`
`rArr angle(C)` is acute angle and `a = b` represents `angleA = angleB`