🏗️ Part (d): Where should I stand?

Move the child along AB. Watch the 3D sight triangle and discover where the angle of elevation to the top of the mast is greatest.

Given

AC = 102 m

∠CAB = 34°

angle of elevation from A = 9°

Point C is the foot of the vertical mast and P is its top.

At A, horizontal distance AC is 102 m.

tan 9° = PC / 102

PC = 102 tan 9° ≈ 16.15 m

Position on AB

A B

Position from A 0.0 m

Distance to C 102.0 m

Mast height PC 16.2 m

Elevation θ 9.0°

The mast height never changes. So what needs to become as small as possible?

tan θ = mast height / ground distance

The dot shows your current position. Notice that the graph rises, reaches one maximum, then falls again.

The shortest distance from point C to the line AB is the perpendicular distance CD.

CD = AC sin 34°

CD ≈ 57.04 m

tan θ_max = 16.15 / 57.04

θ_max ≈ 15.8°

LIVE ANGLE OF ELEVATION

θ = 9.0°

Start at A. Move the orange observer towards B and watch how the sight line changes.

Observer

Mast PC

Line of sight

Perpendicular CD

Drag to rotate • Scroll to zoom • Use the slider to move along AB