Question

Which property can be justified using the ratios in triangle XYZ

Answer 1

The correct answer is B. 

We can actually tell this without even doing work as every answer for Cos(α) = Sin(90 - α) due to the way that Sin and Cos wave behave. However, we can also tell this by using some mathematical evaluation. 

Sin(Y) = Cos(90 - Y)
Sin(50) = Cos(90 - 50)
.766 = Cos(40)
.766 = .766

This should that they are exactly the same. 

Answer 2

Answer:

Option (B) is correct.

$\sin Y= \cos (90^{\circ}-Y)$

Step-by-step explanation:

Given : A figure showing triangle XYZ with right angle at X and measurement of angles and sides are given.

We have to choose the correct option from the given options.

Consider the given options , we will check each one by one.

A)

$\cos Y =\frac{x}{z}$

We know, Cosine of an angle gives the relationship between base and hypotenuse.

$\cos\theta =\frac{base}{hypotenuse}$

Thus, For $\theta=Y$, we have base is z and hypotenuse = x

Thus, $\cos Y =\frac{z}{x}$

So, (A) is false.

B)

$\sin Y= \cos (90^{\circ}-Y)$

We know $\sin\theta= \cos (90^{\circ}-\theta)$

Thus,  $\sin Y= \cos (90^{\circ}-Y)$ is true.

SO, (B) is correct.

C)

$\cos Z= \sin (90^{\circ}-Y)$

We know $\cos\theta= \sin (90^{\circ}-\theta)$

Thus,  $\cos Z= \sin (90^{\circ}-Z)$

SO, (C) is not correct.

D)

$\tan Z=\frac{\cos Y}{\sin Z}$

Since, $\tan Z=\frac{\sin Z}{\cos Z}$

Thus, $\tan Z=\frac{\cos Y}{\sin Z}$ is incorrect.

Thus, Option (B) is correct.