Explanation Formula used: Trigonometric ratios: sin θ = Opposite Hypotenuse ; csc θ = Hypotenuse Opposite cos θ = Adjacent Hypotenuse ; sec θ = Hypotenuse Adjacent tan θ = Opposite Adjacent ; cot θ = Adjacent Opposite Calculation: Assume that ABC and DEF are two right angled triangles with different sizes but with the same acute angle θ . If two triangles have same acute angle θ , then the two triangles are in equal proportion with respect to their sides and hence the triangles are similar. By the above fact, Opposite A B C Opposite D E F = Hypotenuse A B C Hypotenuse D E F (1) The above equation can be rearranged as, Opposite A B C Hypotenuse A B C = Opposite D E F Hypotenuse

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Chapter 8.1, Problem 1ED

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To explain: The reason why the trigonometric ratios of θ is independent of the size of the right triangle.

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Chapter 8.1, Problem 5MP

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Chapter 8 Solutions

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The reason why the trigonometric ratios of θ is independent of the size of the right triangle.

Solution Summary: The author explains how the trigonometric ratios of theta are independent of the size of a right triangle.

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