Answer:
tan y°
Step-by-step explanation:
by using the Sine Rule (See attached), we can form the equation:
[tex]\frac{r}{sin (y)} = \frac{p}{sin (x)}[/tex]
rearranging this, we get:
[tex]\frac{r}{p} =\frac{sin(y)}{sin(x)}[/tex] ---------------------eq 1
Recall that all internal angles of a triangle must sum to 180°. we observe that we have a right triangle where one of the angles is 90°. It then follows that the sum of the other two angles must sum to 90°
i.e x + y = 90°
with a little rearranging, we get
x = (90° - y)
Substituting this into eq 1 above, we get:
[tex]\frac{r}{p} =\frac{sin(y)}{sin(90- y)}[/tex] ---------eq 2
recall that from the trigonometric co-function identities,
sin (90°- y) = cos y
substituting this into eq 2 gives :
[tex]\frac{r}{p} =\frac{sin(y)}{cos(y)} = tan(y)[/tex] (answer)
