medium difficulty6 min

Sketching the situation before solving

Sketching the situation before solving means drawing a simple labelled diagram before writing any trigonometric equation.

In one line: Sketch first, solve second.

Practice This Concept

Understand it

A good sketch is the first tool in application questions.
It helps you identify the observer, object, horizontal line, vertical height, and line of sight.
Once the sketch is ready, the correct angle and trigonometric ratio become much easier to spot.
Many students lose marks because they start with formulas and only later try to imagine the diagram.
In this chapter, sketching is not optional; it is part of the solution method.

Example

For a building problem, a sketch shows the building vertical, the ground horizontal, and the viewer's line of sight slanting upward.

Formula and rule

No separate formula; the sketch helps identify the correct triangle for tan, sin, or cos.

See it worked out

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

Worked example

In a tower problem, a quick sketch immediately shows that the tower is vertical, the ground distance is horizontal, and the angle at the observer decides the ratio.

Method you can reuse

1Read the question slowly.
2Draw a simple diagram.
3Label known lengths and angles.
4Mark the right angle.
5Decide the ratio from the sketch.
6Solve from the labelled figure.

Visual tip

Always draw a labelled right triangle or viewing diagram with horizontal ground, vertical height, and slant line of sight.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is a sketch important before solving a height-and-distance question?

Think first, then show answer

A sketch shows the correct triangle, the angle position, and the sides clearly. It helps you choose the right ratio and avoid mixing up height, distance, and line of sight.

Common wrong answer

A common wrong answer is to start calculations without a diagram. That often leads to wrong side identification and wrong equations.

Don't mix this up

Students often skip the sketch and then mix up the sides or the angle position.

Exam tip

A neat sketch can save marks even if arithmetic is slightly weak, because it shows the correct mathematical setup.

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

Questions may not directly ask for a sketch, but a correct sketch usually supports the full solution and reduces side confusion.

1
Enough for 1 mark
Sketching the situation before solving means drawing a simple labelled diagram before writing any trigonometric equation.
2
Add for 2 marks
Example: For a building problem, a sketch shows the building vertical, the ground horizontal, and the viewer's line of sight slanting upward.
3
Add for 3 marks
Once the sketch is ready, the correct angle and trigonometric ratio become much easier to spot.

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