Question

If the sin of angle x is 4 over 5 and the triangle was dilated to be two times as big as the original, what would be the value of the sin of x for the dilated triangle? Hint—Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no spaces. (4 points)

Answer 1

Explanation:

sin of angle x =
`(4)/(5)`

If the triangle is dilated 2 times - it becomes two time larger.

4 times 2 = 8 and 5 times 2 = 10

So the ratio would be
`(8)/(10)`, which when reduced (divide numerator and denominator by 2) becomes
`(4)/(5)`.

This is correct as dilation changes the size of an image - but not its angles or proportions, meaning ratios remain the same.

So the answer is 4/5.

Answer 2

Sin of x does not change

Explanation:

Whenever a triangle is dilated, the angle remains the same as well as the ratio for sides of triangle. For smshapes with dimensions, when shapes are dilated the dimensions has increment with common factor.

From trigonometry,

Sin(x)=opposite/hypotenose

Where x=4/5

Sin(4/5)= opposite/hypotenose

But we were given the scale factor of 2 which means the dilation is to two times big.

Then we have

Sin(x)=(2×opposite)/(2×hypotenose)

Then,if we divide by 2 the numerator and denominator we still have

Sin(x)=opposite/hypotenose

Which means the two in numerator and denominator is cancelled out.

Then we still have the same sin of x. as sin(4/5)

Hence,Sin of x does not change