Projection Math Example 3

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Example 3

easy
A 55 m flagpole stands vertically. At 33 pm the sun casts a horizontal shadow 1212 m long. What is the length of the shadow (the projection of the pole onto the ground)?

Solution

  1. 1
    Step 1: The shadow is the orthogonal projection of the vertical pole onto the horizontal ground.
  2. 2
    Step 2: The shadow length is given as 1212 m. The pole height (55 m) and shadow (1212 m) form the legs of a right triangle; the sun's ray is the hypotenuse with length 52+122=169=13\sqrt{5^2 + 12^2} = \sqrt{169} = 13 m.

Answer

Shadow (projection) =12= 12 m; sun's ray =13= 13 m.
A shadow is a real-world example of projection — the vertical object is projected onto the horizontal plane by parallel light rays. The pole, shadow, and sun's ray form a right triangle.

About Projection

The image formed when points of a shape are mapped onto a lower-dimensional surface along parallel or converging rays.

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More Projection Examples

Example 1 medium

Find the orthogonal projection of point [formula] onto the [formula]-axis, the [formula]-axis, and t

Example 2 hard

Vector [formula] is projected onto vector [formula]. Find (a) the scalar projection and (b) the vect

Example 4 hard

Project the vector [formula] onto the unit vector [formula] (the [formula]-axis direction). Interpre

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