medium difficulty6 min

Tower and building contexts

Tower and building contexts are word problems in which heights, distances, and angles are related using trigonometry around tall structures.

In one line: Tower height stands up, ground distance lies flat.

Practice This Concept

Understand it

Towers and buildings are the most common objects in this chapter because they naturally create right triangles with the ground.
The vertical side is the height of the structure, the horizontal side is the distance from the observer, and the slant side is the line of sight.
Students should read the wording carefully to decide whether the question gives the height, the distance, or both.
Then choose the proper ratio and solve step by step.

Example

A building is seen from a point 25 m away at 37 degrees. The height above eye level can be found using tan 37 and then adjusted if eye level is given.

Formula and rule

Use tan θ = height / distance for standard level-ground tower and building sketches; adjust for eye level if given.

See it worked out

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

Worked example

1A building is 20 m away from an observer, and the angle of elevation is 45 degrees.
2Then tan 45 = height/20, so the height above the observer's eye is 20 m.

Method you can reuse

1Draw the tower and observer.
2Mark the ground distance.
3Mark the angle.
4Choose tan, sin, or cos based on given sides.
5Solve and check units.
6Mention whether height is from ground or eye level.

Sketch it in your answer

Sketch the tower vertically, the observer on the ground, the horizontal ground distance, and the line of sight to the top.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

In a tower problem, which quantity is usually the vertical side of the triangle?

Think first, then show answer

The vertical side is usually the height of the tower or building. The ground distance is the horizontal side, and the line of sight is the slant side.

Common wrong answer

A common wrong answer is to take the slant distance as the tower height. The slant is longer than the vertical height.

Don't mix this up

Students sometimes mix the building height with the distance from the observer, or forget the eye-level correction.

Exam tip

Write the height, ground distance, and angle separately on your sketch before doing any calculation.

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

Find the height of a tower or building, the distance from it, or the angle of elevation from a given distance.

1
Enough for 1 mark
Tower and building contexts are word problems in which heights, distances, and angles are related using trigonometry around tall structures.
2
Add for 2 marks
Example: A building is seen from a point 25 m away at 37 degrees. The height above eye level can be found using tan 37 and then adjusted if eye level is given.
3
Add for 3 marks
Towers and buildings are the most common objects in this chapter because they naturally create right triangles with the ground.

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