Triangle Street
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how do you find the shadow of a 5 ft tall person if he or she is 30 ft away from a 20 foot tall street light?
the street light and groung make a 90 degree angle and the light from the street lamp and the persons shadow makes a right triangle
This is a basic geometry question which uses the axiom that the ratio of similar triangles are equal. This means that the ratio of the triangle created by the person's shadow and the triangle created by the light with respect to the person should be equal.
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20_________________ |
|___________________5
|________30_________|_____X_______
If the length of the shadow created by the person is equal to
X
then the total distance to the head of the shadow from the light pole will equal
30 + x
Since the ratio of the triangles should be equal we get this equation.
20/(30 + x) = 5/x
Doing the math, you get
20x = 150 + 5x
which simplifies to
15x = 150
which means
x = 10
Therefore, the length of the shadow is 10 feet long.
p.s. People, these ARE NOT congruent triangles. Congruent triangles have three sides that are congruent, meaning equal, and three angles that are congruent. This problem demonstrates the properties of SIMILAR triangles.
Haddon Street Love Triangle
