Geometry and TrigonometryMediumShadow at a 45° sun angle
Geometry and Trigonometry practice question
A vertical flagpole is 12 metres tall. When the sun's rays make a 45° angle with the level ground, how long, in metres, is the flagpole's shadow?
Answer: 12
The pole, its shadow and the sun's ray form a right triangle with a 45° angle, so it is isosceles: the shadow equals the height, 12 metres.
Common wrong answers
- If you answered 6
- 6 halves the height, which would apply to a different angle.
- If you answered 17
- 17 is about 12√2, the length of the sun's ray from the top of the pole to the tip of the shadow — the hypotenuse, not the shadow.
- If you answered 24
- 24 doubles the height; at 45° the two legs are equal.
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