Lesson 23 ·Class 9 · Solution of Right Triangles · Angle Lab
Rocket, Ladder, Kite
Three stories, one triangle. 40 km at 60° to the vertical — how high is the rocket?
Live ratios
θ = 30°
sin θ 1/2
= opp/hyp = 150/300 = 0.500
cos θ √3/2
= adj/hyp = 260/300 = 0.866
tan θ 1/√3
= opp/adj = 150/260 = 0.577
Same triangle, three costumes — θ = 30°
ladder 30 m: reaches 30 sin θ = 15.0 m up
kite, 100 m string: flies 100 sin θ = 50.0 m high
rocket, 40 km leg: climbs 40 sin θ = 20.0 km
height = hypotenuse × sin θ, whatever the costume
Try this
- 1 Drag the ladder's foot in and out — the ladder stays 30 m, the top slides along the wall.
- 2 Snap to 30°: the ladder reaches 30 × sin 30° = 15 m — exactly half its length.
- 3 Snap to 60° and read the card: the same triangle as a kite flies 100 × sin 60° = 50√3 m, and as a rocket climbs 40 × sin 60° km.
Snap
Free play — drag the point and snap the angles. Switch to when you want goals.
The ladder is fixed at 30 m — only the angle changes. Pull the foot out: θ drops and the top slides DOWN the wall. height = 30 × sin θ. Same triangle plays kite (100 × sin θ) and rocket (40 × sin θ).
What this lesson covers
What you do
- Drag the ladder's foot in and out — the ladder stays 30 m, the top slides along the wall.
- Snap to 30°: the ladder reaches 30 × sin 30° = 15 m — exactly half its length.
- Snap to 60° and read the card: the same triangle as a kite flies 100 × sin 60° = 50√3 m, and as a rocket climbs 40 × sin 60° km.
Challenges to clear
- Tilt to 30° above horizontal — the rocket's second stage.
- sin 30° = ½: a 30 m ladder at 30° reaches exactly 15 m.
- Kite string at 60°: height = 100 sin 60° = 50√3 m.
Hint
The ladder is fixed at 30 m — only the angle changes. Pull the foot out: θ drops and the top slides DOWN the wall. height = 30 × sin θ. Same triangle plays kite (100 × sin θ) and rocket (40 × sin θ).