What problems does this solve?
Three common applied types: the angle of elevation (height from distance and angle), a leaning ladder (reach up a wall), and a rotating wheel (seat height at a given time).
// maths › Advanced Applications
Real-World Trig Problems
Solve common applied trigonometry problems — angle of elevation, a leaning ladder, and height on a rotating wheel — with full working, in degrees or radians.
elevation: h = d·tanθ; ladder: h = L·sinθ; wheel: y = D + R·sin(ωt)
Angle unit
Frequently asked questions
Can you show a worked example?
Angle of elevation: a point 20 m away at 35° gives height = 20 × tan 35° ≈ 14.0 m. Switch to radians and 35° becomes ≈ 0.6109 rad with the same result.
How is the ladder problem modelled?
A ladder of length L at angle θ to the ground reaches L sin θ up the wall and sits L cos θ out from it — a right-angle triangle with the ladder as hypotenuse.
How is the rotating wheel modelled?
As y = D + R sin(ωt): centre height D, radius R, angular speed ω and time t. It is the same sinusoidal model used for any circular motion.
Why check the answer is sensible?
A height should be shorter than the hypotenuse, an elevation angle between 0° and 90°, and a wheel seat between the ground and the top of the circle.