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Refer to the figure. Show that α + β = γ, and find tan γ.
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| Photo by Math Principles in Everyday Life |
Solution:
Referring to the given figure above
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| Photo by Math Principles in Everyday Life |
Since the two small triangles are right triangles, then we can get the other angle of two triangles as follows
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| Photo by Math Principles in Everyday Life |
The two vertices of a big triangle are vertical angles with the other two triangles. The sum of the interior angles of a big triangle is calculated as follows
Therefore,
Consider again the figure above
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| Photo by Math Principles in Everyday Life |
We can get the tangent of α and β as follows
If
Take tangent on both sides of the equation, we have
Substitute the values of tan α and tan β to the above equation
Therefore,
