Trigonometric Problems

In these lessons, we will learn the trigonometric functions (sine, cosine, tangent) and how to solve word problems using trigonometry.

Hints on solving trigonometry problems:

• If no diagram is given, draw one yourself.
• Mark the right angles in the diagram.
• Show the sizes of the other angles and the lengths of any lines that are known
• Mark the angles or sides you have to calculate.
• Consider whether you need to create right triangles by drawing extra lines. For example, divide an isosceles triangle into two congruent right triangles.
• Decide whether you will need the Pythagorean theorem, sine, cosine or tangent.
• Check that your answer is reasonable. The hypotenuse is the longest side in a right triangle.

Cosine

Example:  

Calculate the value of cos θ in the following triangle.

Solution:

Use the Pythagorean theorem to evaluate the length of PR.

Tangent

Example: 

Calculate the length of the side x, given that tan θ = 0.4

Solution:

Sine

Example: 

Calculate the length of the side x, given that sin θ = 0.6

Solution:

Using the Pythagorean theorem:

Solve Word Problems using Trigonometry

The following video shows how to use the trigonometric ratio, tangent, to find the height of a balloon.

This video shows how to use the trigonometric ratio, sine, to find the elevation gain of a hiker going up a slope.
A hiker is hiking up a 12 degrees slope. If he hikes at a constant rate of 3 mph, how much altitude does he gain in 5 hours of hiking?