The ladder, wall, and ground form a right triangle. The height up the wall is opposite the $53^{\circ }$ angle, and the 9-foot distance from the wall is adjacent to the angle. Use tangent:

So,

Using $\tan (53^{\circ })\approx 1.33$,

This is about $11.9$ feet, so the correct answer is B.

Use tangent because the horizontal distance and the vertical rise from the ranger's eyes to the top of the cliff are related by the angle of elevation. Let $h$ be the height of the cliff. Then

So

Using $\tan (38^{\circ })\approx 0.781$,

Add the ranger's eye height:

The closest answer is $68$.

Since $\tan A=\frac{3}{4}$, substitute into the expression:

Find the sum in the denominator:

Now divide:

So the equivalent expression is $\frac{9}{25}$.

The angle of elevation and the horizontal distance form a right triangle, where the building's height is the side opposite the $35^{\circ }$ angle and the distance from the building is the adjacent side. Use tangent:

So,

Using a calculator,

Thus,

So the height of the building is closest to $84$ feet.

Since $\tan \theta =\frac{1}{12}$, the ratio of rise to run is $\frac{1}{12}$. The horizontal distance is the run, so if the run is $18$ feet, then the rise is $\frac{1}{12}\cdot 18=1.5$ feet. The ramp is the hypotenuse of the right triangle, so use the Pythagorean theorem:

Therefore, the ramp length is closest to $18.1$ feet.