The string, the ground, and the kite’s height form a right triangle. The 80-foot string is the hypotenuse, and the height of the kite is opposite the $53^{\circ }$ angle. Use sine:

so

Since $\sin (53^{\circ })\approx 0.80$, the height is about

Therefore, the kite is approximately $64$ feet above the ground.

The situation forms a right triangle. The drone's flight path from $A$ to $B$ is the hypotenuse, with length 220 feet. The horizontal distance from point $A$ to the base of the cliff is adjacent to the $35^{\circ }$ angle.

Use cosine:

So,

Multiply both sides by 220:

Using a calculator,

Rounded to the nearest foot, the horizontal distance is $180$ feet.

Since $\sin A=\frac{5}{13}$, the side opposite angle $A$ can be represented as $5$ and the hypotenuse as $13$. In a right triangle, the adjacent side is found using the Pythagorean theorem: $\sqrt{13^2-5^2}=\sqrt{169-25}=\sqrt{144}=12$. Therefore, $\tan A=\frac{\text{opposite}}{\text{adjacent}}=\frac{5}{12}$. So the equivalent expression is $\frac{5}{12}$.

Since the longer leg is opposite the angle and $\tan (\theta )=\frac{3}{4}$, the ratio opposite:adjacent must be $3:4$. The longer leg is $x+3$, so it must correspond to 4 parts, and the shorter leg $x$ must correspond to 3 parts. This gives

Solve:

So the legs are $9$ and $12$. A right triangle with legs in the ratio $3:4$ has hypotenuse in the corresponding ratio $5$, so the triangle is a $3$-$4$-$5$ multiple. Since the scale factor is $3$, the hypotenuse is $5\cdot 3=15$. You can also verify with the Pythagorean theorem:

The situation forms a right triangle. The ground distance from the pole to the anchor point is 15 feet, and the wire makes a $53^{\circ }$ angle with the ground, so the 15-foot side is adjacent to the angle. The height of the pole is opposite the angle. Using tangent,

Solving gives

Therefore, the statement that must be true is choice A.