medium difficulty6 min

Choosing suitable trig ratio

Choosing suitable trig ratio means selecting sin, cos, tan, cot, sec, or cosec based on the sides or angles given in the problem.

In one line: Sides first, ratio second.

Practice This Concept

Understand it

The correct ratio depends on which sides are known and which side is required.
If the question involves height and ground distance, tan is often best.
If the hypotenuse is involved, sin or cos may be better.
The important habit is to identify opposite, adjacent, and hypotenuse correctly before writing any ratio.
Many errors happen because students choose a ratio by memory instead of by geometry.

Example

If height and distance are given, tan is used. If height and slant side are given, sin may be used. If base and slant side are given, cos may be used.

Formula and rule

tan = opposite/adjacent, sin = opposite/hypotenuse, cos = adjacent/hypotenuse; choose the ratio that matches the given sides.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

1A question gives the height of a pole and the distance from its base.
2Since these are the opposite and adjacent sides, tan is the proper ratio.

Method you can reuse

1Draw the triangle.
2Label the given sides.
3Identify the unknown side.
4Match the sides with a trigonometric ratio.
5Write the equation.
6Solve carefully.

Sketch it in your answer

Mark opposite, adjacent, and hypotenuse on a small triangle before deciding the ratio.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

If a problem gives the height of a tree and the ground distance from it, which ratio is usually best?

Think first, then show answer

Tan is usually best because it connects the vertical height and the horizontal ground distance directly in a right triangle.

Common wrong answer

A common wrong answer is to use sine just because the word trigonometry appears. The ratio must fit the sides, not the chapter name.

Don't mix this up

Students often choose the ratio they remember first, even when it does not match the given sides.

Exam tip

Ask one question before solving: Which two sides are linked by the data? That answer tells you the ratio.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Choose the correct ratio for a given situation, or explain why a certain ratio is appropriate in a height-distance question.

1
Enough for 1 mark
Choosing suitable trig ratio means selecting sin, cos, tan, cot, sec, or cosec based on the sides or angles given in the problem.
2
Add for 2 marks
Example: If height and distance are given, tan is used. If height and slant side are given, sin may be used. If base and slant side are given, cos may be used.
3
Add for 3 marks
The correct ratio depends on which sides are known and which side is required.

MCQ Quiz

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