Lesson 52 ·Class 10 · Heights and Distances · Field Lab

The Lighthouse Keeper

Midnight, 180 m up. A boat radios: "how far out are we?" — you answer with a table.

🚩 reef ends · 200 myou — the keeper180 m⛵325 m out↓ 29°00′open water — radio the distance ✓
The scene, solved live
midnight. A fishing boat radios the lighthouse: "how far out are we?" You have no radar — only the dip of your gaze and a four-figure table.
your gaze dips 29°00′
table: tan 29°00′ = 0.5543
distance = 180 ÷ 0.5543 = 325 m
"you are 325 m out — open water" (tan 29° = 0.5543, the book case ✓)
Try this
  1. 1 Night watch: drag the boat. Your gaze's dip reads in degrees + minutes — real instruments, not famous angles.
  2. 2 The boat calls from a 29° dip: tan 29° = 0.5543 → 180 ÷ 0.5543 ≈ 325 m. Radio back: open water.
  3. 3 A current pulls it to the red reef flag (200 m out): the dip steepens to 41°59′ — the same table, read backwards. Any closer and it's on the rocks.
Snap

Free play — drag the scene — observer, boat, sun or cloud — and watch the numbers follow. Switch to when you want goals.

From 180 m up: distance = 180 ÷ tan(dip). tan 29° = 0.5543 → 325 m; at the 200 m reef line the dip is 41°59′.
Hold to talk

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