Question

How do you use trigonometric ratios to solve word problems?

Answer 1

Hint: The trigonometric ratios help in solving problems related to triangles.
Steps to solve the word problems based on trigonometric ratios:
If no diagram is given, draw the diagram.
Mark the right angle in the diagram.
Show the sizes of the other angles and the length of any lines that are known.
Mark the angles or sides that we have to calculate.
Consider whether we need to create the right triangles by drawing extra lines.
Decide whether we will apply the Pythagorean theorem, sine, cosine, or tangent.
Calculate the answer.

Complete step-by-step answer:
To use the trigonometric ratios to solve the word problem, we should follow some steps.
First, understand the question and draw the appropriate diagram. These are the two most important things to be done in solving the word problems in trigonometry.
 Then if it is possible, we have to split the given information. Because when we split the given information into parts, we can understand them easily.
We have to draw diagrams almost for all of the word problems in trigonometry. The diagram we draw for the given information must be correct. Drawing a diagram for the given information will give us a clear understanding of the question.
After having drawn the appropriate diagram based on the given information, we have to give the name for each position of the diagram using the English alphabets. Giving names for the positions would be easier for us to identify the parts of the diagram.
Now, we have to use the three trigonometric ratios that are sin, cos, and tan function to find the unknown side or angle.

Note:
Hence, if any word problem can be reduced to solving a triangle that can be solved by using trigonometric ratios.
The trigonometric ratios are:
$\sin \theta = \dfrac{{opposite - side}}{{hypotenuse}}$
$\cos \theta = \dfrac{{adjacent - side}}{{hypotenuse}}$
$\tan \theta = \dfrac{{opposite - side}}{{adjacent - side}}$