Answer: ∠A ≈ 44.42
Step-by-step explanation:
Since this is a right triangle, as given by the little square, we can use trigonometric functions to solve for the missing angle. We are given the adjacent side and the hypotenuse, so we will use the cosine function.
[tex]\boxed{\text{Cosine function}\; \; \rightarrow\;\; cos\theta=\frac{\text{Adjacent}}{\text{Hypotenuse}} }[/tex]
Cosine function:
[tex]cos\theta=\dfrac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
Substitute given values:
[tex]cos(\angle A)=\dfrac{AC}{AB}[/tex]
[tex]cos(\angle A)=\dfrac{5}{7}[/tex]
Take the inverse cosine of both sides:
[tex]arccos(cos(\angle A))=arccos(\dfrac{5}{7})[/tex]
[tex]\angle A=arccos(\dfrac{5}{7})[/tex]
Compute:
[tex]\angle A= 44.415308579521[/tex]
Round to the nearest hundredth:
∠A ≈ 44.42
