WILL GIVE MEDAL!

Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?

A right triangle is shown. The two angles that are not 90 degrees are marked x and y. The leg across from angle y measuring 12, another leg across from angle x measuring 5, and the hypotenuse measuring 13.

The ratios are opposites (negative 5 over 13 and 5 over 13).
The ratios are both identical (5 over 13 and 5 over 13).
The ratios are reciprocals (5 over 13 and 13 over 5).
The ratios are both negative (negative 13 over 5 and negative 13 over 5).

Question

WILL GIVE MEDAL!

Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?

A right triangle is shown. The two angles that are not 90 degrees are marked x and y. The leg across from angle y measuring 12, another leg across from angle x measuring 5, and the hypotenuse measuring 13.

 The ratios are opposites (negative 5 over 13 and 5 over 13).
 The ratios are both identical (5 over 13 and 5 over 13).
 The ratios are reciprocals (5 over 13 and 13 over 5).
 The ratios are both negative (negative 13 over 5 and negative 13 over 5).

impxssive · Answer

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impxssive · Answer

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impxssive · Answer

@phi

imstuck · Answer

Ok, the sin of an angle is the side opposite the angle over the hypotenuse.  Because these sides have lengths in integers, you will have a fraction representing the side opposite/hypotenuse.  What is the side length opposite the x?

impxssive · Answer

12? i am confused on how to find the side length opposite the x @IMStuck

imstuck · Answer

oh!  Well, let's fix that!

imstuck · Answer

|dw:1470261779585:dw|

imstuck · Answer

That is the side opposite.

imstuck · Answer

|dw:1470261843194:dw|

impxssive · Answer

ohh okay so would the fraction be 5/1? @IMStuck

imstuck · Answer

Then of course the longest side is always the hypotenuse.

impxssive · Answer

the hypotenuse is 13, correct? @IMStuck

imstuck · Answer

The 5 is correct, because the sin of an angle is side opposite over hypotenuse.  The 5 represents the side opposite the x.  What is the length of the hypotenuse?

imstuck · Answer

Yes.  So what is the sin of x?

impxssive · Answer

5/13 @IMStuck

imstuck · Answer

yes!! Good!

imstuck · Answer

Now for the cos of y.  The cos of an angle is represented by the side adjacent to the angle over the hypotenuse.  Let's look at the triangle again.

imstuck · Answer

|dw:1470262043194:dw|

imstuck · Answer

The arrow represents the side adjacent to the angle y.  As you can see, it is also the 5, right?

imstuck · Answer

And what did we say the hypotenuse was?

impxssive · Answer

the hypotenuse is 13 and so the arrow adjacent to the angle y should be 12 if i am understanding correctly @IMStuck

imstuck · Answer

No the arrow is pointing to the side with the length of 5.  Adjacent means next to.

imstuck · Answer

Are you familiar with SOHCAHTOA?

impxssive · Answer

it's been quite some time so i am a little rusty @IMStuck

imstuck · Answer

sin is the side opposite the angle/hypotenuse
cos is the side adjacent to the angle/hypotenuse
tan is the side opposite the angle/side adjacent to the angle

imstuck · Answer

The side adjacent to the angle y is the side that is 5.  And the hypotenuse is 13.  So the cos of angle y = 5/13.  What did we say the sin of angle x was?  Scroll up and look.

impxssive · Answer

5/13 as well @IMStuck

imstuck · Answer

Yes!  So they are the same, aren't they!?

imstuck · Answer

Which choice is that one?

jhonyy9 · Answer

very nice job @IMStuck - great your explication is very easy understandably GOOD very very

imstuck · Answer

Why, thank you, @jhonyy9 !!

impxssive · Answer

B  The ratios are both identical (5 over 13 and 5 over 13).

imstuck · Answer

Very awesome job!

impxssive · Answer

:) Thank you for your help! I really do appreciate it :D @IMStuck