Problem Solving with Trigonometric Functions

Many application problems involving right triangles use words like angle of depression and angle of elevation. The angle of depression is angle measured below the horizontal, and may also be called the angle of declination. The angle of elevation is the angle measured above the horizontal (see figure below), and may also be called the angle of inclination.

Let’s start with a couple of basic angle of elevation problems:

The next example is a little more complex than the ones shown above, since it involves working with more than one right triangle and it’s an angle of depression problem. See if you can solve the question on your own before viewing its solution:

Finally, not all trigonometric ratio problems you encounter will be angle of elevation or depression-based. Here’s an example involving two right triangles facing one another.

Now that you’ve seen several examples, try answering the questions underneath. Post your solutions in the comments section.

Question 1.

To find the height of a flagpole (shown below), a person measures 35.0 ft from the base of the pole and then measures an angle of 40.8° from a point 6.00 ft above the ground to the top of the pole. Find the height of the flagpole.

Question 2.

After leaving port, a ship holds a course N 46° 12′ E for 225 M (nautical miles). Find how far north and how far east of the port the ship is now located.

Source: Technical Mathematics with Calculus, 3e. Calter & Calter.