Answer:
[tex]A\approx 28^{\circ}[/tex]
Step-by-step explanation:
Please find the attachment.
We have been given that area of triangle ABC is 3√2 square inches.
[tex]\text{Area}=\frac{1}{2}\text{Base}\times \text{height}[/tex]
We know that area of triangle an be found using trigonometry as:
[tex]\text{Area}=\frac{1}{2}\times c\times h[/tex]
[tex]\text{sin}(A)=\frac{h}{9}\\h=9\cdot \text{sin}(A)[/tex]
[tex]3\sqrt{2}=\frac{1}{2}\times 2\times 9\cdot \text{sin}(A)[/tex]
[tex]3\sqrt{2}=9\cdot \text{sin}(A)[/tex]
[tex]9\cdot \text{sin}(A)=3\sqrt{2}[/tex]
[tex]\text{sin}(A)=\frac{3\sqrt{2}}{9}[/tex]
[tex]\text{sin}(A)=\frac{\sqrt{2}}{3}[/tex]
Now, we will use inverse sine to find the value of angle A as:
[tex]A=\text{sin}^{-1}(\frac{\sqrt{2}}{3})[/tex]
[tex]A=28.1255057^{\circ}[/tex]
[tex]A\approx 28^{\circ}[/tex]
Therefore, the measure of angle A is approximately 28 degrees.
