If the cos of angle x is eight seventeenths and the triangle was dilated to be two times as big as the original, what would be the value of the cos of x for the dilated triangle?

Answer 1

A dilated triangle is similar to the original, so all of the angles are the same. Hence cos x for the dilated triangle would be equal to the cos x for the original (8/17). Here's why:

For the original, cos x = adjacent / hypotenuse = 8/17

For the dilated triangle, the adjacent side and the hypotenuse are twice as long. Hence

cos x = 2·adjacent / 2·hypotenuse. But the 2s cancel and you get cos x = adjacent / hypotenuse = 8/17.

The value of Trig functions depend only on the angle, not on the size of the triangle.