Can u guys verify that this is correct.

If i have a triangle with sides 8, 11 and 17, would the length of the altitude drawn to the SMALLEST side be 10.99 or 11

/ \
8 / \11
/ ___ \
17


i used Sin and Cos to find out the measures of each of the angles which turned out to be

111.61
/ \
40.32____28.07

then to solve for the altitude from the vertex of 11 and 17 to 8 (which would be the smallest side)
i did

Sin 40.32 = alt/17 SOH(opposite/hypotenuse)
\ /
17 * Sin(40.32) = alt

and arrived at 10.99 or 11

would this be a way to solve it?

Thanks