A triangle has sides in the ratio of 5:12:13. What is the measure of the triangle's smallest angle in degrees?
The ratio is 5:12:13, so assume a base of 1unit, then a triangle with the sides lengths of 5, 12 and 13 fulfills this ratio.
first check if this triangle has one 90deg angle.
13 as the length of the third side, so it has 90deg angle.
cos(alpha)=adjacent / hypotenuse
alpha=acos(adjacent / hypotenuse)=acos( 12/13 )
[input]acos( 12/13 )[/input]
about 22deg. (and it is the smallest because 180-90-22=68>22)