Answer: The last choice is correct [tex]\frac{9}{\sin\left(60\right)}[/tex]
Step-by-step explanation: The information given in the diagram: AB is the hypotenuse of a right triangle, and the side opposite the 60° angle is 9 feet. you can use sine = 0pposite/Hypotenuse
You can find the sine of 60° which is the value of the ratio of the opposite side to the (unknown) hypotenuse. sin 60° = 0.866
You can set up the equation on a scientific calculator as [tex]\frac{9}{\sin\left(60\right)}[/tex] but to see the logic use the value 0.866 = 9/h
reorganize to solve for h: divide both sides by 0.866 and multiply both by h to get
h = 9/0.866 solving that you get the length of AB
h = 10.393, which, rounded, is a logical length for the brace on the gate:
10.4 feet
