A 195 cm person casts a 2.1 m shadow in the light of a street lamp. If the person is standing 4.2 m from the light, how tall is the light?
To find the height of the street lamp, we can use similar triangles. Here's how you can do it:
Step 1: Identify the similar triangles
In this scenario, we have two similar triangles. One triangle is formed by the person, their shadow, and the distance between the person and the lamp. The other triangle is formed by the street lamp, its own shadow, and the distance between the person and the lamp.
Step 2: Set up the proportion
Let's set up a proportion using the heights and shadows of the person and the street lamp:
(person's height) / (person's shadow) = (lamp height) / (lamp shadow)
In this case, we know the person's height is 195 cm (or 1.95 m), the person's shadow is 2.1 m, and the distance between the person and the lamp is 4.2 m. We need to solve for the lamp height.
Step 3: Solve for the lamp height
Using the proportion we set up in step 2, we can plug in the values we have:
1.95 m / 2.1 m = (lamp height) / (lamp shadow)
Simplifying the equation:
1.95 / 2.1 = (lamp height) / 4.2
To solve for the lamp height, we can cross-multiply and then divide:
(1.95 / 2.1) * 4.2 = lamp height
Calculating the result:
(1.95 * 4.2) / 2.1 = lamp height
8.19 / 2.1 = lamp height
lamp height ≈ 3.9 m
Therefore, the height of the street lamp is approximately 3.9 meters.