What is the measure of angle A?

#"since all 3 sides are given there is a choice of trig ratios"#
#"we can use"#

#"that is sine, cosine or tangent"#

#angleA=sin^-1(4/5)=53.13^@#

#angleA=cos^-1(3/5)=53.13^@#

#angleA=tan^-1(4/3)=53.13^@#

We have a few ways to solve this.

We have for angle A:

#tan(A)="opposite"/"adjacent"=4/3#

#sin(A)="opposite"/"hypotenuse"=4/5#

#cos(A)="adjacent"/"hypotenuse"=3/5#

Using the inverse functions:

#A=arctan(4/3)=53.13010235^@=53.13^@# nearest hundredth

#A=arcsin(4/5)=53.13010235^@=53.13^@# nearest hundredth

#A=arccos(3/5)=53.13010235^@=53.13^@# nearest hundredth

As expected they all give the same result. When given enough information, you can use which ever one you want.