A 6-foot person standing 15 feet from a streetlight casts a 15-foot shadow. Two similar triangles are formed. One triangle is formed by the person and the shadow that the person casts. A second triangle is formed by the streetlight and the ground from the base of the streetlight to the end of the shadow.
The street light is ___ times taller than the person
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Theanswer is 25
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To determine the height of the streetlight in relation to the person, we can use the property of similar triangles.
Similar triangles have the same shape but can differ in size. Two triangles are similar if their corresponding angles are equal, and their corresponding sides are in proportion.
Let's assign some variables to the known information:
- Height of the person: P = 6 feet
- Distance from the person to the streetlight: D1 = 15 feet
- Length of the person's shadow: S1 = 15 feet
- Height of the streetlight: S = unknown
Now, we can set up a proportion using the ratio of corresponding sides in the two similar triangles:
(P / S1) = (S / (D1 + S1))
Plugging in the values we know:
(6 / 15) = (S / (15 + 15))
Simplifying the equation:
(2/5) = (S / 30)
To find S, the height of the streetlight, cross-multiply and solve for S:
2 * 30 = 5 * S
60 = 5S
S = 60 / 5
S = 12
Therefore, the streetlight is 12 times taller than the person.