Question

A triangle ABC is such that sin(2A + B) =1/2 . If A, B, C are in A.P. then the angle A, B, C are

Answer 1

Answer:

A,B,C ARE 45° ,60°,75°

Step-by-step explanation:

sin(2A+B) = 1/2

2A+B =sin `¹ (1/2)

2A+B = 30 (or) 150 ------(1)

In a triangle sun of interior angles is equal to 180

A+B+C = 180 ------(2)

Given ,

A,B,C are in A. P

then 2B = A+C --------(3)

put ,

(3) in(2)

2B +B = 180

3B = 180

B = 60°

If B is 60 then 2A + B = 30 is not possible

So,

2A + B = 150

2A + 60 = 150

2A = 90

A = 45°

put A= 45 and B = 60 in (2)

45+60+C = 180

105 + C = 180

C = 75°