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Hello,Welcome to StudentBro.
Hello,Welcome to StudentBro.
Height and distance problems are an essential application of trigonometry in JEE Maths. These problems involve calculating the heights of objects, distances between objects, and angles of elevation and depression. At StudentBro.in, we provide a comprehensive guide with formulas, solution methods, examples, and practice questions to help JEE aspirants master height and distance problems efficiently for JEE Main & Advanced exams.
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Height and distance problems are trigonometric applications that involve:
Finding the height of objects like poles, towers, or buildings
Calculating distances between objects using angles of elevation and depression
Applying right triangle trigonometry in real-world scenarios
Example: From a point 50 m away from a tower, the angle of elevation to the top is 30°. Find the height of the tower.
The angle of elevation is the angle formed by the line of sight of an observer looking upwards to an object above the horizontal line.
Formula using a right triangle:
tan θ = Opposite / Adjacent = Height / Distance
Important for calculating heights of buildings, trees, or towers
Example: If tan 30° = h / 50 → h = 50 × tan 30° = 50 × (1/√3) ≈ 28.87 m
The angle of depression is the angle formed by the line of sight of an observer looking downwards from a height to an object on the ground.
Similar formula applies:
tan θ = Opposite / Adjacent = Height / Distance
Widely used in coastal, airport, and observation tower problems
Example: If an observer sees a boat at 45° depression from a lighthouse 100 m tall → distance = 100 / tan 45° = 100 m
tan θ = Height / Distance
Height = Distance × tan θ
Distance = Height / tan θ
For two objects or multiple points of observation:
Use difference of heights and angles
Apply right triangle rules systematically
When an observer views the top of a tower from two different points on the same horizontal line, the height can be found using:
Formula:
h=d1d2(tanθ1−tanθ2)d2−d1h = \frac{d_1 d_2 (\tan θ_1 - \tan θ_2)}{d_2 - d_1}h=d2−d1d1d2(tanθ1−tanθ2)
Where d1, d2 are distances from the tower and θ1, θ2 are angles of elevation
Example:
Observer sees the top of a tower at 30° from point A (20 m from tower) and 60° from point B (40 m from tower). Height: h = ...
Real-life applications in engineering, construction, surveying, and navigation
Helps in calculating tower heights, tree heights, and distances between objects
Applied in physics problems on projectile motion and inclined planes
Draw a clear right triangle diagram with height, distance, and angle
Label all known and unknown quantities
Use tan θ = Height / Distance systematically
For multiple points of observation, apply difference method or ratio method
Solve previous JEE problems for speed and accuracy
At StudentBro.in, students can access:
Step-by-step explanations for angles of elevation and depression
Worked examples for single and two-point observations
Practice questions with solutions and shortcuts
Tips for quick diagram drawing and formula application
Revision notes for last-minute preparation
From a point 30 m away from a tower, the angle of elevation to the top is 45°. Find the height of the tower.
The angle of depression from a 50 m tall building to a car on the ground is 30°. Find the distance of the car from the base.
An observer sees the top of a tower at 30° from one point and 60° from another point 50 m farther. Find the height of the tower.
A man 2 m tall is 10 m away from a wall. Find the angle of elevation to the top of the wall.
Two poles of heights 10 m and 15 m are 30 m apart. Find the angle of elevation to the top of the taller pole from the top of the shorter pole.
Regular practice improves accuracy, speed, and confidence in solving height and distance problems in JEE exams.
Height & Distance problems are a vital application of trigonometry in JEE Maths. Understanding angles of elevation, angles of depression, and right triangle formulas allows students to calculate heights and distances efficiently. At StudentBro.in, we provide a complete guide from basics to advanced problem-solving, making these problems easy, practical, and exam-oriented.
Mastering this topic ensures students can tackle all height and distance problems confidently in both JEE Main and Advanced exams.
