The measure of angle A to the nearest degree is 30°
Explanation:
The triangle is right angled, so we would apply trigonometry ratio SOHCAHTOA
Angle = A
opposite = side opposite angle A = 8 feet
hypotenuse = longest side = 16 ft
adjacent = base = ?
Now, since we know the opposie and hypotenuse, we would use sin ratio (SOH):
[tex]\sin A=\frac{opposite}{hypotenuse}[/tex][tex]\begin{gathered} \sin \text{ A = }\frac{8\text{ f}eet}{16\text{ f}et} \\ \sin \text{ A =}\frac{\text{ 1}}{2} \end{gathered}[/tex]
Take inverse of sine:
[tex]\begin{gathered} A=sin^{-1}(\frac{1}{2}) \\ A\text{ = }sin^{-1}(0.5) \\ A=\text{ 30}\degree \end{gathered}[/tex]
The measure of angle A to the nearest degree is 30°
