To calculate: The range of values of side a of a triangle ABC such that it has two solutions, one solutions and no solution provided
Answer to Problem 45E
The range of values of side a of a triangle ABC is provided below,
Explanation of Solution
Given information:
The criteria for number of solutions provided
Formula used:
The table for number of solutions,
Calculation:
Consider a triangle ABC with
Case I: When
The side a is very short to complete the triangle and reach the base of it. As observed no triangle exists, so there is no solution.
Case II: When
The side a is perpendicular to the base of the triangle. As observed it is a right angled triangle and one triangle is possible, so there is one solution.
Case III: When
The side a touches the base of triangle at two points. As observed there are two triangles so there are two solutions possible.
Case IV: When
The side a touches the base of the triangle at a single point. As observed one triangle is possible, so there is one solution.
Consider criteria for number of solutions provided
It is provided that
The triangle ABC has no solution if
The triangle ABC has one solution if
Also the triangle ABC has one solution if
The triangle ABC has two solutions if
The range of values of side a of a triangle ABC is provided below,
Chapter 6 Solutions
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