Question

What is the measure of angle A?

Answer 1

`angleA=53.13^@`

Explanation:

`"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^@`

Answer 2

`color(blue)(53.13^@)`

Explanation:

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.