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Heights and Distances Practice Questions with Detailed Solutions – Level 2

Medium-level heights and distances practice on two-angle setups: walking observers, ships seen from lighthouses, flagstaffs on buildings, eye-level corrections and changing shadows, with worked steps.

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Questions, answer key and solutions.

Questions
50
Duration
60 min
Marks
50

Negative marking

Attempts
100
Access
Free
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Both use the same questions. Normal practice is untimed and needs no account: choose an option and the answer and solution appear at once. The Simulated test is the real computer-based format, with one 60-minute clock, a question palette and full screen, and your score, the key and the solutions arrive when you submit.

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The computer-based test format: one clock, a question palette, and a score the moment you submit.

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About this test

Heights and Distances Level 2 Practice Quiz: Two-Angle and Moving Observer Problems

Built for students who already know the basic trigonometric ratios, Heights and Distances Level 2 on Aptitude360 is a practice set of two-step problems. It covers observers walking towards towers, ships seen from a lighthouse, flagstaffs on buildings, statues on pedestals, eye-level adjustments and shadows that change with the sun's altitude.

What the Level 2 heights and distances problems test

  • Height of a tower when the angle of elevation changes as an observer walks towards it
  • Ships, boats or cars on the same side or on opposite sides of a lighthouse or tower
  • Elevation of a tower's top and depression of its foot from the top of a building
  • Flagstaffs on buildings and statues on pedestals seen from one ground point
  • Eye-level and hand-height corrections for observers and kite flyers
  • Shadow ratios at different sun altitudes, similar shadows, aeroplane speed and sliding ladders

Formulas and rules for two-angle height problems

  • Tangent ratio: \( \tan\theta=\dfrac{\text{height}}{\text{base}} \)
  • Distance walked, \( \alpha<\beta \): \( d=h\left(\dfrac{1}{\tan\alpha}-\dfrac{1}{\tan\beta}\right) \)
  • Height from that walk: \( h=\dfrac{d\tan\alpha\tan\beta}{\tan\beta-\tan\alpha} \)
  • Complementary angles from distances \( a,b \): \( h=\sqrt{ab} \)
  • Similar shadows: \( \dfrac{h_{1}}{s_{1}}=\dfrac{h_{2}}{s_{2}} \)

Preparation tips for medium-level heights and distances

  • When two angles appear, write one tangent equation for each triangle and eliminate the shared horizontal distance.
  • Subtract the observer's eye height or the hand height from the total height before applying a ratio.
  • For a flagstaff or statue, find the building or pedestal height first, then the extra height from the second angle.
  • For moving objects, find the distance covered between the two positions, then divide by the time to get speed.

Who this set is meant for

This middle stage of the series is best taken after the basic level by quantitative aptitude learners ready for problems that combine two triangles.

FAQs about Heights and Distances Practice Questions with Detailed Solutions – Level 2

How do you solve heights and distances problems involving two angles?
Write a tangent equation for each right-angled triangle, keeping the height common. Then eliminate the unknown horizontal distance between the two equations to find the height or the gap.
What happens to the shadow when the sun's altitude decreases?
The shadow becomes longer as the sun's altitude decreases. The length of the shadow equals the height divided by the tangent of the sun's altitude, and tangent falls as the angle gets smaller.
How do you account for the observer's height in heights and distances?
Measure the angle from the observer's eye level, so the triangle's height is the object's height minus the eye height. Add the eye height back at the end if the full height of the object is asked.
Is heights and distances asked in aptitude tests?
Yes, heights and distances appears as an application of trigonometry in many quantitative aptitude sections. Problems usually test the standard ratios and two-triangle setups.

Test structure

How the paper is split, and how long each part runs. A section you have finished cannot be returned to.

SectionQuestionsTime
Heights and Distances Level 25060 min

Marking & rules

Total marks
50 across 50 questions.
Negative marking
A wrong answer costs marks. Leaving a question unanswered costs nothing.
Attempts
100 in total. An attempt is spent the moment you begin one.

What you get when you submit

The analysis is ready the moment you submit the paper.

Score and accuracy

Marks, percentage, right, wrong and skipped, and the time you took.

Section by section

The same figures for each section, so a weak one cannot hide in an average.

The full answer key

Every question with your answer, the right one, the working, and the video where there is one.

Where you stand

Your score against the spread of everyone else who has sat this test.

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