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.
16°
Problem:
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.
Solution:
Step 1: Use the sum of angles in a triangle:
The sum of the angles in a triangle is always 180°.
Let the angles be 17x, 13x, and 15x, where x is the common multiple.
17x + 13x + 15x = 180
Simplify:
45x = 180
Solve for x:
x = 180 ÷ 45 = 4
Step 2: Calculate the three angles:
- The largest angle = 17x = 17 × 4 = 68°
- The smallest angle = 13x = 13 × 4 = 52°
- The middle angle = 15x = 15 × 4 = 60°
Step 3: Find the positive difference between the largest and smallest angles:
68° − 52° = 16°
Final Answer:
The positive difference between the largest and smallest angles is 16°.
Important Questions from Co-ordinate Geometry
The graphs of the linear equations 4x - 2y = 10 and 4x + ky = 2 intersect at a point (a, 4). The value of k is equal to:
In which ratio the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3)?
The area (in sq. units) of the triangle formed by the graphs of 8x + 3y = 24, 2x + 8 = y and the x-axis is:
In which quadrant both abscissa and ordinate are negative?
Find the slope of the line joining the points (3, -4) and (5, 2).
