Question

If tan x° = 11 divided by r and cos x° = r divided by s, what is the value of sin x°?

Answer 1

$\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse} \quad % tangent tan(\theta)=\cfrac{opposite}{adjacent}\\\\ -------------------------------\\\\ tan(x^o)=\cfrac{11}{r}\cfrac{\leftarrow opp}{\leftarrow adj}\qquad cos(x^o)=\cfrac{r}{s}\cfrac{\leftarrow adj}{\leftarrow hyp}\\\\\\ \boxed{sin(x^o)=\cfrac{11}{s}\cfrac{\leftarrow opp}{\leftarrow hyp}}$

Answer 2

Answer:

$sin x = \frac{11}{s}$

Step-by-step explanation:

$Tan x = \frac{11}{r}$

$Cos x = \frac{r}{s}$

Property : $\frac{sin \theta}{cos \theta}=Tan \theta$

So, $\frac{sinx}{cosx}=Tan x$

Substitute the values

$\frac{sinx}{ \frac{r}{s}}=\frac{11}{r}$

$sinx =\frac{11}{r} \times \frac{r}{s}$

$sinx =\frac{11}{s}$

Hence the value of sin x° is $\frac{11}{s}$