Answer:
[tex]\displaystyle \sin A=\frac{1}{3}[/tex]
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of the triangle is called the hypotenuse and the other two sides are called the legs.
We are given a triangle with side lengths of 3, [tex]\sqrt{72}[/tex], and 9, where 9 is the hypotenuse. Before applying the trigonometric ratios, we must check if the triangle is right, and the Pythagora's theorem is satisfied:
[tex]9^2=3^2+(\sqrt{72})^2[/tex]
81=9+72=81
Now we're sure it's a right triangle, we apply the sine formula:
[tex]\displaystyle \sin A=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]
The opposite leg to A is 3, and the hypotenuse is 9, then:
[tex]\displaystyle \sin A=\frac{3}{9}[/tex]
Simplifying:
[tex]\boxed{\displaystyle \sin A=\frac{1}{3}}[/tex]
