Right Triangle Trigonometry
Solving word problems involving trig ratios can be tricky, especially if you have
no illustration to guide you. So, we must try to draw are own and use that as our
guide.
One thing of note, is to be aware of how the angle is described, such that you
know where to place it on the triangle. If you have an angle of elevation, it refers
to the horizontal and the line of sight, which is upwards.
Object being viewed
Angle of elevation
(your position)
In the event of an angle of depression, it refers to the horizontal and the line of
sight, which is downwards.
Angle of elevation (your position)
Object being viewed
Example:
A helicopter hovers 800ft directly above a small island, just at the water’s edge.
From the helicopter, the pilot takes a sighting to a boat directly offshore. If the
angle of depression is 35° , how far from the coast is the boat?
Answer:
If you draw a right triangle, it might look something like the following:
35°
Helicopter
800 ft
Angle of depression
Boat
Island
NOTE The 35° is labeled outside of the triangle, which is fine. Just remember
that its point of view as when you are looking downwards from the horizon. It’s
never measured from the vertical.
Using Geometry, you can see that the angle, 35° , is also the angle being made
in the triangle where the boat is located. We now have a triangle with all the
labels that are given.
Right Triangle Trigonometry
800 ft
35°
x
Here we can use tangent to find the value for x, which is the distance between
the island and the boat.
tan 35° =
800
x
800
tan 35°
≈ 1140ft
x=
NOTE Instead of using the angle next to the boat, which is 35° , you could have
taken the angle inside the triangle where the helicopter is located to be 55° , and
solved giving the same result.