Concept explainers
(a)
To describe: A triangle for the given sum of the angles.
(a)
Explanation of Solution
Introduction:
Sum of all the interior angles of a triangle is
As shown in the figure below, a triangle is drawn on the sphere. Considering one vertex on the North Pole and the other two vertices on the latitude of the sphere. Such that, the other two angles will be a right angle, and due to the curvature of the sphere, the lines of the triangle will be curved outwards. This makes the third angle of
If such a triangle is formed on the curvature of the sphere, then the sum of the limiting angles would be
Conclusion:
A triangle is drawn whose two vertices on the latitude lines and the third one on the North Pole.
(b)
To describe: A triangle for the given sum of the angles.
(b)
Explanation of Solution
Introduction:
Sum of all the angles in a triangle is
If a triangle is drawn on the surface of a sphere, then due to the curvature of the sphere, the sum of angles would be greater than
Conclusion:
Thus, a triangle drawn on a flat surface has the sum of
Chapter 33 Solutions
Physics: Principles with Applications
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