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The measures of the three angles of a triangle are in the ratio 17 : 13 : 15. Find the positive difference between the greatest and the smallest of these three angles.
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The measures of the three angles of a triangle are in the ratio 17 : 13 : 15.
Formula Used:
Sum of angles in a triangle = 180º
Let the measures of the three angles be 17x, 13x, and 15x.
Calculation:
Sum of the angles = 17x + 13x + 15x
17x + 13x + 15x = 180º
⇒ 45x = 180º
⇒ x = 180º / 45
⇒ x = 4º
The greatest angle = 17x = 17 × 4º = 68º
The smallest angle = 13x = 13 × 4º = 52º
The positive difference between the greatest and the smallest angle = 68º – 52º = 16º
The correct answer is option 1.