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In a right-angle triangle, perpendicular is [math]\sqrt{3}[/math] times the base. What is ratio of their opposite angles?
In a right-angle triangle, perpendicular is [math]\sqrt{3}[/math] times the base. What is the ratio of their opposite angles?
The opposite angles of a right-angle triangle are complementary, which means they add up to 90 degrees. As for the ratio, let me work it out for you. If the base is 'b', then the perpendicular is [math]\sqrt{3}b[/math]. Using the tangent function, we can find that one of the angles is [math]tan^{-1}\sqrt{3}[/math] and the other is [math]tan^{-1}\frac{1}{\sqrt{3}}[/math]. Therefore, the ratio of their opposite angles is [math]tan^{-1}\sqrt{3} : tan^{-1}\frac{1}{\sqrt{3}}[/math].