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In a right triangle, the sine of angle α, which we write as “sin α,” is defined as the length of the side opposite the angle divided by the length of the hypotenuse.

You may have seen this before as “the sine is the opposite over the hypotenuse.”

In this triangle, sin α = a/c.

We’re now going to dilate this triangle. Let’s refer to the image of angle α as angle α′.

First, use a scale factor bigger than 1. What happens to sin α′ as the triangle gets larger?

Second, use a scale factor between 0 and 1. What happens to sin α′ as the triangle gets smaller?

Explain your answer using the postulates and theorems covered in this unit.

Answer:

joshalex768 Mar 14, 2019

#1**+2 **

I don't know what unit you are in, so this may differ than other answers. Dilation preserves angles, but not side lengths. However, all side lengths are reduced or extended by the same ratio, so the ratio of sides will remain the same. So no matter the scale factor, sin α′ will remain the same.

Hope this helps!

LagTho Mar 14, 2019

#1**+2 **

Best Answer

I don't know what unit you are in, so this may differ than other answers. Dilation preserves angles, but not side lengths. However, all side lengths are reduced or extended by the same ratio, so the ratio of sides will remain the same. So no matter the scale factor, sin α′ will remain the same.

Hope this helps!

LagTho Mar 14, 2019