Question

If $\tan \theta =\frac{15}{8},$ then the value of $\frac{17}{4}\cos \theta$ is

• A. 8
• B. 15
• C. 2
• D. 17

Answer 1

The correct option is C 2

Given: $\tan =\frac{15}{8}$

In a right triangle,

$\tan =\frac{\text{Perpendicular (P)}}{\text{Base (B)}}=\frac{15}{8}$



Let P = 15 k and B = 8k
(where k is any positive integer)

By Pythagoras theorem,

$H^2=P^2+B^2$

$=(15k{)}^2+(8k{)}^2$

$=225k^2+64k^2$

$=289k^2$

$\Rightarrow H=17k$

$\therefore \cos \theta =\frac{B}{H}=\frac{8k}{17k}=\frac{8}{17}$

$\Rightarrow \frac{17}{4}\cos \theta =$

$\Rightarrow \frac{17}{4}\times \frac{8}{17}=2$

Hence, the correct answer is option c.