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The measures of the angles of a triangle are in the ratio 3:7:8. Find their measures in degrees and radians. - Mathematics and Statistics

Sum

The measures of the angles of a triangle are in the ratio 3:7:8. Find their measures in degrees and radians.

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Solution

The measures of the angles of the triangle are in the ratio 3:7:8.

Let the measures of the angles of the triangle in degrees be 3k, 7k and 8k, where k is a constant.

∴ 3k + 7k + 8k + 8k = 180°    ...[Sum of the angles of a triangle is 180°]

∴ 18k = 180°

∴ k = 10°

∴ The measures of the angles in degrees are

3k = 3° x 10° = 30°,

7k = 7° x 10° = 70° and

8k = 8° x 10° = 80°.

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

∴ The measures of the angles in radians are

30° = `(30 xx pi/180)^"c" = (pi/6)^"c"`

70° = `(70 xx pi/180)^"c" = ((7pi)/18)^"c"`

80° = `(80 xx pi/180)^"c" = ((4pi)/9)^"c"`

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