Question

angles of triangles are in AP. if the number of degrees is smallest to the the no of radian is the largezt as tge 60:π.then the smallest angle is
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Answer 1

Solution :

The three angles in A.P.

if y is common difference, let these angles be

(x + y) , x and (x − y)

∴ x + y + x + x − y = 180

x = 60

According to the question,

(x - y)/(x + y)π/180 = 60/π

π(x − y) = (x + y)π/180 x 60

3(x − y) = x + y

4y = 2x

y = x/2

∴ y = 60/2

y = 30

=> Smallest angle is 30 and Hence three angles are 30 , 60 , and 90

Answer 2

The three angles in A.P.; if y is common difference,

let these angles be (x+y) ∘ ,x ∘ and(x−y) ∘ ∴x+y+x+x−y=180∘

x=60∘

According to the question,

{(X-Y) / (X+Y)π^c/180°} = 60/π

π(X-Y) = (X+Y) π/180 × 60

3(X-Y) =(X+Y)

4Y = 2X

∴y/2=60 ∘

=30 ∘

Hence three angles are 30 ∘ ,60 ∘ and 90 ∘ .