Question

Look at the figure if tan x=3/y and cos x =y/z what is the value of sin x?

Answer 1

Answer: sin x° = 3/z( answer

Because tan is opposite/adjacent,

Cos is adjacent/hypotenuse and sin is opposite/hypotenuse the information to find sin is given. You simply take the opposite (3) and put it over the hypotenuse (z)

sin x°= 3/z

Answer 2

Recall:

The tan of the measure of an angle is the ratio of the opposite side to the adjacent side to that angle, that is :

$\displaystyle{ \tan x^{\circ}= \frac{opposite\ side}{adjacent \ side}$. 

Since this ratio is 3/y, we denote the opposite side, and adjacent side respectively by 3 and y. 

(Technically we should write 3t and yt, but we try our luck as we see y in the second ratio too!)


Similarly, $\displaystyle{\cos x^{\circ}= \frac{adjacent\ side}{hypothenuse}$.


The adjacent side is already denoted by y, so we denote the length of the hypotenuse by z.



Now the sides of the right triangle are complete. 

$\displaystyle{ \sin x^{\circ}= \frac{opposite\ side}{hypotenuse}= \frac{3}{z}$


Answer: A