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Question
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 = 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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