Answer:
The measure of the smallest angle is [tex]22.6\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle ABC
[tex]tan(A)=\frac{BC}{AB}[/tex]
substitute
[tex]tan(A)=\frac{12}{5}[/tex]
[tex]A=tan^{-1}(\frac{12}{5})= 67.4\°[/tex]
Find the measure of angle C
Remember that
[tex]m<A+m<C=90\°[/tex] ------> by complementary angles
[tex]m<C=90\°-67.4\°=22.6\°[/tex]
