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Question

The difference between the two acute angles of a right - angled triangle is 2π5 radians. Express the angles in degrees.

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Solution

Let θ1 and θ2 be two acute angles of a right angled triangle.

different of acute angles

θ1θ2=2π5 radians

in a right angled triangle,

θ1+θ2=π2

θ1θ2=2π5 . . .(i)

θ1+θ2=π2 . . . (ii)

On solving

2θ1=2π5+π2

θ1=9π20

From equation (ii)

θ2=π20

So angles in degrees

θ1=9π20×180π=81

and θ2=π20×180π=9


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