The rod $AC$ of a TV disc antenna is fixed at right angle to the wall $AB$ and a rod $CD$ is supporting the disc as shown in the given figure. If $AC = 1.5$ m long and $CD = 3$ m, find (i) $ an het

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The rod $AC$ of a TV disc antenna is fixed at right angle to the wall $AB$ and a rod $CD$ is supporting the disc as shown in the given figure. If $AC = 1.5$ m long and $CD = 3$ m, find (i) $	an 	heta$ (ii) $\sec 	heta + \csc 	heta$.

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Accepted Answer

Step 1: $\cos 	heta = \frac{AC}{CD} = \frac{1.5}{3} = \frac{1}{2} \Rightarrow 	heta = 60°$
(i) $	an 	heta = 	an 60° = \sqrt{3}$
(i) Alternatively: $\sin 	heta = \frac{AC}{CD} \Rightarrow \sin 	heta = \frac{1}{2} \Rightarrow 	heta = 30°$
$	an 30° = \frac{1}{\sqrt{3}}$
Step 2: (ii) $\sec 	heta + \csc 	heta = \sec 30° + \csc 30° = \frac{2}{\sqrt{3}} + 2 = \frac{2\sqrt{3} + 6}{3}$

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