Question

In the figure, $AD = DB$, $\angle B$ is a right angle and $\angle BCD = 	heta$, $AC = b$ and $AB = a$. Then $	an	heta$ is equal to

Accepted Answer

B. In right $	riangle ABC$, $BC = \sqrt{AC^2 - AB^2} = \sqrt{b^2 - a^2}$. Since $AD = DB$ and $AB = a$, $BD = \frac{a}{2}$. In right $	riangle DBC$, $	an	heta = \frac{BD}{BC} = \frac{a/2}{\sqrt{b^2 - a^2}} = \frac{a}{2\sqrt{b^2 - a^2}}$.

Trigonometric ratio in right triangle

Explanation

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