medium difficulty8 min

Ratio interpretation from diagram

Ratio interpretation from a diagram means reading a right-triangle sketch correctly and deciding which trig ratio the marked sides represent.

In one line: The angle decides the names, not the drawing alone.

Practice This Concept

Understand it

Diagrams in trigonometry are meant to help, but they can also mislead if the angle is not marked carefully. The same triangle can give different opposite and adjacent sides depending on which acute angle is chosen. Correct reading of the diagram is the key exam skill.

Example

In a right triangle with angle A marked at one acute corner, the side across from A is opposite, the side next to A is adjacent, and the longest side is the hypotenuse.

Formula and rule

Opposite and adjacent are always measured with respect to the chosen acute angle; the hypotenuse is opposite the right angle and does not change.

See it worked out

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

Worked example

If angle A is at the left corner, the bottom side may be adjacent.

1If angle A is moved to the top corner, that same bottom side may become opposite.
2The labels depend on the angle.

Method you can reuse

1Find the right angle.
2Mark the angle asked in the question.
3Name the hypotenuse.
4Name the opposite side.
5Name the adjacent side.
6Match the ratio.

Sketch it in your answer

Use a clean right-triangle sketch with the right angle marked clearly. Then label sides separately for each acute angle if needed.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

In a right triangle, if angle A changes to the other acute angle, what happens to opposite and adjacent sides?

Think first, then show answer

The labels change with the angle. A side that was opposite for one angle can become adjacent for the other angle. The hypotenuse stays the same, but opposite and adjacent depend on the chosen angle.

Common wrong answer

A common wrong answer is to assume the bottom side is always adjacent. That is false when the angle changes position.

Don't mix this up

Students often label the same side as opposite for one angle and then reuse it for another angle without checking the new reference angle.

Exam tip

Before writing the ratio, trace the chosen angle with your finger and relabel all three sides from that point.

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

CBSE may ask students to identify sides from a figure, select the correct ratio from a labeled diagram, or detect a mislabelled side.

1
Enough for 1 mark
Ratio interpretation from a diagram means reading a right-triangle sketch correctly and deciding which trig ratio the marked sides represent.
2
Add for 2 marks
Example: In a right triangle with angle A marked at one acute corner, the side across from A is opposite, the side next to A is adjacent, and the longest side is the hypotenuse.
3
Add for 3 marks
Diagrams in trigonometry are meant to help, but they can also mislead if the angle is not marked carefully.

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