QQuestion
The difference of acute angles of a right angled triangle is 72°. Determine these acute angles in circular measure
WBBSEClass 10MathematicsConcept of Measurement of Angle03 Mark2024 Moderate
✓Answer
Let the two acute angles of a right-angled triangle be x and y (in degrees).
Since the sum of all angles in a triangle is 180°, and one angle is 90°,
we have
x + y = 90° …(i)
It is given that the difference of the acute angles is 72°,
so,
x – y = 72° …(ii)
Adding (i) and (ii):
2x = 162°
∴ x = 81°
Substitute the value of x in (i):
81° + y = 90°
∴ y = 9°
Now, convert the angles into circular measure (radians):
x = 81° × π \over 180 = 9π \over 20 radians
y = 9° × π \over 180 = π \over 20 radians
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