In ancient Egypt, when the Nile flooded, it often erased the boundaries between landowners. An accurate surveying process was necessary in-order to re-establish property lines. Land surveyors used Pythagoras' theorem to verify that property lines were correctly drawn by calculating how long they should be.

Two farmers occupy a property that is in the shape of a rectangle. Their property line is the diagonal of the rectangle. Find the length (in $\mathrm{m}$)of the property line if the sides of the property measure $48 \mathrm{m}$ and $55 \mathrm{m}$.

 

Subduction is a process where a heavier oceanic plate plunges underneath a lighter continental plate. The process can be either deep or shallow, depending on the angle of subduction. In very old subduction zones, a mountain range, called a volcanic arc, is formed directly above the point where the heavier plate reaches a depth of $100 \mathrm{km}$. A deep trench along the boundary of two plates is also formed.

A volcanic arc is located a horizontal distance of $250 \mathrm{km}$ from the trench.

Find the angle of subduction (in degrees). Round your answer to the nearest tenth of a degree.

Airport meteorologists keep an eye on the weather to ensure the safety of airplanes. One thing they watch is the cloud ceiling. The cloud ceiling is the lowest altitude at which solid cloud is visible.If the cloud ceiling is too low, the planes are not allowed to take off or land.

One process a meteorologists can use to find the cloud ceiling at night is to shine a searchlight that is located a fixed distance from her office vertically into the clouds. Then, she measures the angle from the office to the spot of light on the cloud.

The search light is located $40 \mathrm{m}$ from the office.

If the angle to the spot of light on the cloud is $38$ degrees, how high (in m)is the cloud ceiling?(Round the answer in nearest tenths place)