## anonymous one year ago The figure below shows a right triangle What is r ÷ p equal to? tan y° sin y° tan x° sin x°

1. anonymous

2. mathstudent55

Do you know SOHCAHTOA, the side length ratios of sine, cosine, and tangent?

3. princeharryyy

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4. anonymous

no im not to familiar with it

5. anonymous

@welshfella can u help me please??

6. mathstudent55

The sine, cosine, and tangent ratios of a right triangle are as follows: $$\sin A = \dfrac{opp}{hyp}$$ $$\cos A = \dfrac{adj}{hyp}$$ $$\tan A = \dfrac{opp}{adj}$$

7. mathstudent55

Let's see how the sine ratio applies to a right triangle.

8. mathstudent55

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9. mathstudent55

Look at the figure above. For angle A, leg AC is called the adjacent leg. For angle A, leg BC is the opposite leg. The hypotenuse is side AB.

10. mathstudent55

According to the definition of sine, $$\sin A = \dfrac{opp}{hyp}$$ the sine of angle A is the ratio of the lengths of the opposite leg to the hypotenuse. That means that for the figure above, $$\sin A = \dfrac{BC}{AB}$$

11. mathstudent55

Do you understand how the sine function works?

12. anonymous

yes i do thank you (:

13. mathstudent55

Now let's look at your problem. We are asked what the ratio r/p is equal to.

14. mathstudent55

r and p are legs of the triangle. The only ratio (of sin, cos, and tan) that deals only with the lengths of legs (and not the hypotenuse) ids the tangent ratio. $$\tan A = \dfrac{opp}{adj}$$ The tangent ratio is the ratio of the lengths of the opposite leg to the adjacent leg.

15. mathstudent55

The ratio r/p must be a tangent because it involves only lengths of legs. Since the ratio r/p must be a tangent, it must be equal to $$\dfrac{opp}{adj}$$ Now we look in the figure, and we see which angle is opposite leg r? It is angle y. Also, we look in the figure and we see that leg p is the adjacent leg top angle y. The means we must have the tangent of angle y.

16. anonymous

oh ok i understand now thank you so much, (: btw @mathstudent55 the answer to the question would be (A) right? (:

17. mathstudent55

yes

18. mathstudent55

You're welcome.