In a right angled triangle, the acute angles are in the ratio 4:5. Find the angles of the triangle in degrees and radians.

#### Solution

Since the triangle is a right angled triangle, one of the angles is 90°.

In the right angled triangle, the acute angles are in the ratio 4:5.

Let the measures of the acute angles of the triangle in degrees be 4k and 5k, where k is a constant.

∴ 4k + 5k + 90° ...[Sum of the angles of a triangle is 180°]

∴ 9k = 180° – 90°

∴ 9k = 90°

∴ k = 10°

∴ The measures of the angles in degrees are

4k = 4 x 10° = 40°,

5k = 5 x 10° = 50°

and 90°

We know that θ° = `(theta xx pi/180)^"c"`

∴ The measures of the angles in radians are

40° = `(40 xx pi/180)^"c" = ((2pi)/9)^"c"`

50° = `(50 xx pi/180)^"c" = ((5pi)/18)^"c"`

90° = `(90 xx pi/180)^"c" = ((pi)/2)^"c"`