Real-Life Math
You decided to go to university to study geomatics engineering because
you enjoy math and computers. Plus, you didn't want to be stuck in a
cubicle.
Your friend Sam feels the same way. That's why the two
of you were so happy to get placements at the same company, Evanston Surveys
Ltd., for your first co-op work term. And now you're a team.
The
two of you are heading out to survey the route for a new highway. This is
your first real hands-on assignment.
It's chilly and raining and
the mud is splashing up to your knees. You're pretty sure you've
just invented cement pants. But at least your equipment is state of the art
and will still work in the rain.
Sam heads off up the hill with the
rod while you stand in place with the electronic theodolite, which must be
perfectly level. A theodolite is an instrument that measures horizontal and
vertical angles.
Your lightweight theodolite has a 30X telescope. It
reads angles in less than a second by aiming at the bottom and the top of
the rod and straight ahead. Once you know these angles, the theodolite calculates
distance and slope.
Your theodolite has a self-checking microprocessor,
so its measurements should be accurate. It uses formulas from trigonometry
to calculate distance and slope, among other things.
Height
of the rod = 6.5 feet
Height of the theodolite = 5 feet
The
theodolite gives you the following readings:
Angle a =
3.43 degrees
Angle b = 5.71 degrees
height = 14.7 feet
distance
= 164.2 feet
Oh no! Your supposedly weatherproof theodolite
has just conked out because of the rain! You have to calculate the slope yourself.
Good thing you understand how the theodolite calculates slope.
Using
the following equation, find the percentage slope of the hill.
slope
= height / distance x 100