Welcome to Heights and Distances! 🏔️
Discover the Power of Trigonometry
Learn how to measure heights and distances without actually climbing or walking there! Master angle of elevation, angle of depression, and solve real-world problems.
Angle of Elevation
Angle formed when looking UP from horizontal to an object above you. Measured upward from the horizontal line.
Angle of Depression
Angle formed when looking DOWN from horizontal to an object below you. Measured downward from the horizontal line.
Line of Sight
Imaginary straight line connecting the observer's eye to the object being viewed.
tan(θ) Formula
tan(θ) = Height/Distance
Most commonly used ratio for heights and distances problems.
Most commonly used ratio for heights and distances problems.
Right Triangle
Every heights and distances problem forms a right-angled triangle with horizontal, vertical, and line of sight.
Key Ratios
sin(θ) = Opposite/Hypotenuse
cos(θ) = Adjacent/Hypotenuse
tan(θ) = Opposite/Adjacent
cos(θ) = Adjacent/Hypotenuse
tan(θ) = Opposite/Adjacent
Common Angles
tan(30°) = 1/√3
tan(45°) = 1
tan(60°) = √3
tan(45°) = 1
tan(60°) = √3
Problem Steps
1. Draw diagram
2. Identify right triangle
3. Choose correct ratio
4. Solve for unknown
2. Identify right triangle
3. Choose correct ratio
4. Solve for unknown
Applications
Measure heights of buildings, towers, mountains, and distances across rivers without direct measurement.