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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.

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete 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.

  4. 4

    Avoid this incomplete 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.

Definition

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

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.

Rule to remember

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

Memory hook

Sides first, ratio second.

Examples and method

Worked example

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

Method to apply

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

Diagram support

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

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.

Avoid common mistakes

Common confusion

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

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.

Exam tip

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

Quick check

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

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

Answer writing and exam use

1-mark answer

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

2-mark answer

Choosing suitable trig ratio means selecting sin, cos, tan, cot, sec, or cosec based on the sides or angles given in the problem. tan = opposite/adjacent, sin = opposite/hypotenuse, cos = adjacent/hypotenuse; choose the ratio that matches the given sides. 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-mark answer

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. tan = opposite/adjacent, sin = opposite/hypotenuse, cos = adjacent/hypotenuse; choose the ratio that matches the given sides. A question gives the height of a pole and the distance from its base. Since these are the opposite and adjacent sides, tan is the proper ratio. Choose the correct ratio for a given situation, or explain why a certain ratio is appropriate in a height-distance question. A common wrong answer is to use sine just because the word trigonometry appears. The ratio must fit the sides, not the chapter name.
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