Question

If the cos of angle x is 5 over 8 and the triangle is dilated to be three times as big as the original, what would be the value of the cos of x for the dilated triangle?

15 over 24
10 over 16
5 over 8
The cos value cannot be determined for the dilated triangle.

Answer 1

Given :cos x = 5/8

we know that,
in a dilatation the angles do not change

example
in a right triangle

cos x = Adjacent side angle x/Hypotenuse
So,
When the triangle is dilated by 3
the adjacent side will be dilated to 15 and the Hypotenuse will be dilated to 24
which means 5/8 will become 15/24
and hence,
15/24 after simplifying will be 5/8.
Thus there is no change

the answer is the option
5/8