Question

if the sin of angle x is 4/5 and the triangle was dilated to be two times as big as the orginal, what would be the value of the sin of x for the dilated triangle

Answer 1

There will be no change. It will still be 4/5

Explanation:

When one performs a dilation of a triangle, all sides get affected. In this case, since the dilation is by a factor of two, the sides will double their lengths.

But recall that dilations will create similar triangles, which means that their angles at the vertices remain the same.

The trig functions of angles depend only on the actual angle they are applied to, so, since the angles remain the same, the sine value will stay the same: "4/5".