PHISICOS

Lighthouse Rescue: Aim with Angles

An educational simulation game. Turn side ratios into angles with tan⁻¹, sin⁻¹, and cos⁻¹, and fly the drone to the ship.

Inverse functionsElevation and depression

COAST / SIDE VIEW

Angle of depression

Ready
Enable JavaScript to fly the drone. The instructions and worked example remain readable.
Drone velocity vHorizontal: D and vₓVertical: H and v_yLine of sight rShip or lamp target
Velocity componentsv = 10 m/s

Time

0.00 s

t

Drone position

(0.0, 0.0) m

r = (x, y)

Drone velocity

(0.00, 0.00) m/s

v = (vₓ, v_y)

Distance flown

0.0 m

s = |v| · t

Angle below the horizontal

—

tan⁻¹(|v_y| ÷ |vₓ|)

Find the angle or the distance

Name the sides relative to the marked angle. To find an angle from two sides, use an inverse function: tan⁻¹, sin⁻¹, or cos⁻¹.

Fly the rescue drone to its target.

Mission score—

Choose the angle of depression so the drone reaches the sea within 5 m of the ship.

✓ Target reached (within 5 m)◎ Precise to 1%

How to play Lighthouse Rescue

  1. Choose a mission and read its givens. Find the marked angle and the horizontal or vertical line it is measured from.
  2. Name the sides relative to that angle: opposite, adjacent, and hypotenuse.
  3. To find an angle, calculate the ratio of two sides and apply tan⁻¹, sin⁻¹, or cos⁻¹. To find a side, rearrange the ratio.
  4. Type your answer and press Play. The drone flies in a straight line and shows whether your answer reaches the target.

Inverse functions turn ratios back into angles

Sine, cosine, and tangent take an angle and give a ratio of sides. Their inverse functions, sin⁻¹, cos⁻¹, and tan⁻¹, take a ratio and give back the angle. An angle of depression is measured down from the horizontal at the observer; an angle of elevation is measured up from the horizontal. Because the two horizontals are parallel, the depression from the lamp equals the elevation from the ship.

A focused learning model

The drone flies in a straight line at a constant 10 m/s, with no wind, take-off, or braking, and its size is ignored. The sea is flat and the Earth's curvature is ignored, which is reasonable over a few hundred metres. Heights are measured from sea level. Playback runs 4 times faster than real time.

Changing language keeps your mission, answer, and flight.