Question 952470
Using Law of Cosines:
k=side opposite K=20ft; l=side opposite L=10ft; m=side opposite M=15ft 
{{{cos(M)=(k^2+l^2-m^2)/(2kl)}}}
{{{cos(M)=(20ft^2+10ft^2-15ft^2)/2(20ft)(10ft)}}}
{{{cos(M)=(400ft^2+100Ft^2-225ft^2)/(400ft^2)}}}
{{{cos(M)=(275ft^2)/(400ft^2)}}}=0.6875
Angle M={{{cos^-1(0.6875)=46.6degrees}}}
ANSWER: Measure of angle M is 47 degrees.