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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

Given:
Difference between two acute angles of a right-angled triangle = 2π5 rad
1 rad=180π°

2π5 rad=180π×2π5° =36×2° =72°

Now, let one acute angle of the triangle be x°.
Therefore, the other acute angle will be 90°-x°.
Now,
x°-90°-x°=72°x-90+x=722x=162x=81
Thus, we have:
x° = 81°
And,
90°-x° = 90°-81° = 9°

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