Question

if tan theta = 12/5, then 5 sin theta - 12 cos theta =?

Answer 1

hope it shell help u

Answer 2

The value of $5\sin \theta-12\cos \theta$ is "option B) zero(0)".

Step-by-step explanation:

We have,

$\tan \theta=\dfrac{12}{5}$

To find,  $5\sin \theta-12\cos \theta=?$

∴ $\tan \theta=\dfrac{12}{5}=\dfrac{p}{b}$

$h=\sqrt{12^{2}+5^{2}} =\sqrt{144+25}$

$=\sqrt{169}=13$

Where, b = base, p = perpendicular and h = hypotaneous

∴ $\sin \theta=\dfrac{p}{h}=\dfrac{12}{13}$ and

$\cos \theta=\dfrac{b}{h}=\dfrac{5}{13}$

∴ $5\sin \theta-12\cos \theta$

$=5\times \dfrac{12}{13}-12\times \dfrac{5}{13}$

$=\dfrac{60}{13}-\dfrac{60}{13}$

= 0

Hence, the value of $5\sin \theta-12\cos \theta$ is "option B) zero(0)".