Answer: Maria is right. The kite is 265 feet above the ground.
Step-by-step explanation: The question explains first that the string is being held 5 feet above the ground, which implies that whatever is mathematically calculated would be added to 5 feet to get the total height of the kite from the ground.
The kite is held in such a way that it stretches out full length at 300 feet and in the process, forms a 60 degree angle of elevation with the point parallel to the ground. What this means is that a right angled triangle has been formed with one side measuring 300, and the reference angle measuring 60 degrees. The height of the kite above the ground, would be the line facing the reference angle, which is yet unknown.
So what you have is an opposite side h (which is unknown), an hypotenuse which is 300, and a reference angle which is 60°. Maria used a trigonometric ratio, since she had an opposite and an hypotenuse plus a reference angle. The ratio which uses the opposite and hypotenuse is Sine of an angle which is given as;
Sin ∅ = opposite/hypotenuse
Sin 60 = h/300
By cross multiplication you now have
Sin 60 x 300 = h
0.866 x 300 = h
259.8 = h
h ≈ 260
The height is approximately 260 ft + 5 ft for a total of 265 ft.
Billy could not have used Cosine and gotten a correct answer because the rule of trigonometry when applied to Cosine of an angle is given as;
Cosine ∅ = Adjacent/Hypotenuse
The adjacent is the line between the right angle and the reference angle, and in this instance happens to be the line parallel to the ground.