Heights and Distances Practice Questions with Detailed Solutions – Level 1

Heights and Distances Level 1 Practice Questions on Elevation and Depression

Heights and Distances Level 1 on Aptitude360 is a beginner practice set that applies basic trigonometry to angles of elevation and depression. The questions use standard angles in familiar setups: towers, shadows, ladders, kite strings, boats seen from cliffs and trees broken in a storm. Every question has a worked solution.

What this Heights and Distances Level 1 set covers

• Height of a tower or pole from a known distance and angle of elevation
• Shadow length at a given sun altitude, and finding the sun's angle from a shadow
• Ladders against walls, taut wires and kite strings, where the slant length is the hypotenuse
• Angles of depression of boats and cars seen from lighthouses, cliffs and buildings
• An observer walking towards a tower as the angle of elevation changes
• Objects on opposite sides of a tower, a building and a tower viewed together, shadow proportions and a tree broken by a storm

Key trigonometry formulas for heights and distances

• Tangent: \( \tan\theta=\dfrac{\text{height}}{\text{base}} \)
• Sine: \( \sin\theta=\dfrac{\text{height}}{\text{hypotenuse}} \)
• Cosine: \( \cos\theta=\dfrac{\text{base}}{\text{hypotenuse}} \)
• Tangent of thirty degrees: \( \tan 30^{\circ}=\dfrac{1}{\sqrt{3}} \)
• Tangent of sixty degrees: \( \tan 60^{\circ}=\sqrt{3} \)
• Sine of sixty degrees: \( \sin 60^{\circ}=\dfrac{\sqrt{3}}{2} \)

Revision tips for angles of elevation and depression

• Draw a right triangle for every question and label the height, the base and the given angle before choosing a ratio.
• Use tangent when the height and the ground distance are involved. Use sine or cosine when a ladder, string or wire is involved.
• The angle of depression from the top equals the angle of elevation from the ground point, because they are alternate angles.
• Keep answers in surd form with root three until the final step. This makes them easy to match with the options.

Who should take this Level 1 practice set

This set is for students starting heights and distances who want to build basics with standard angles before moving to tougher multi-step problems in quantitative aptitude.