question_answer

If \[\theta \] be acute angle and \[\cos \theta =\frac{15}{17},\]then the value of \[(90{}^\circ -\theta )\]is

A) \[\frac{2\sqrt{8}}{15}\]

B) \[\frac{8}{15}\]

C) \[\frac{\sqrt{2}}{17}\]

D) \[\frac{8\sqrt{2}}{17}\]

Correct Answer: B

Solution :

[b] Given,\[\cos \theta =\frac{15}{17}\] \[\therefore \]Perpendicular \[(AB)=\sqrt{{{17}^{2}}-{{15}^{2}}}\] \[=\sqrt{289-225}\] \[=\sqrt{64=8}\] \[\therefore \]      \[\cot \,(90{}^\circ -\theta )=tan\theta =\frac{8}{15}\]