question_answer

The length of the shadow of a pole inclined at \[10{}^\circ \] to the vertical towards the sun is 2.05 meters,  when the elevation of the sun is \[38{}^\circ .\] The length of the pole is

A) \[\frac{2.05\sin 38{}^\circ }{\sin 42{}^\circ }\]

B) \[\frac{2.05\sin 42{}^\circ }{\sin 38{}^\circ }\]

C) \[\frac{2.05\cos 38{}^\circ }{\cos 42{}^\circ }\]

D) None of these

Correct Answer: A

Solution :

[a] \[\frac{\sin 38{}^\circ }{l}=\frac{\sin (SPO)}{2.05}\] \[=\frac{\sin (180{}^\circ -38{}^\circ -90{}^\circ -10{}^\circ )}{2.05}\] \[\Rightarrow l=\frac{2.05\sin 38{}^\circ }{\sin 42{}^\circ }\]