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Make up three problems involving oblique triangles.
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Answer to Problem 63AYU
Explanation of Solution
Given information
Make up three problems involving oblique triangles. One should result in one triangle, the second in two triangles, and the third in no triangle.
Calculation:
Let us consider an oblique triangle
By using low of sine in the given oblique triangle, we get
Taking first two in
It means this choice of angle
By the property of triangle, we get
From
Hence, it forms only one triangle figured as:
Let us consider an oblique triangle
By using low of sine for the given oblique triangle, we get
Taking first two in
And if
It means both choices of the angle
For
For
From
From
Hence, there can be two triangle form, given as
Let us consider the triangle
Taking first and last, we get
It is never be possible for a triangle. There can be no any triangle form from such given information; the given information can be figure as:
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