A man is 1.9m tall and he stands 2.4m from the lampost , which is 3.2m high. Find the lenght of the man's shadow.
Is your last name Gallo
To find the length of the man's shadow, we can use similar triangles. Let's consider the man, the lamppost, and their shadows as one set of parallel lines intersected by the sun's rays.
Here's the step-by-step explanation to find the length of the man's shadow:
1. Draw a diagram: Draw vertical lines to represent the man, lamppost, and their shadows. Label the man's height as 1.9m, the distance between the man and the lamppost as 2.4m, and the height of the lamppost as 3.2m.
2. Identify the corresponding sides: In the diagram, you can see that the height of the lamppost and the length of its shadow form one pair of corresponding sides, while the height of the man and the length of his shadow form another pair.
3. Set up a proportion: To solve for the length of the man's shadow (let's call it x), set up a proportion by comparing the corresponding sides:
(Man's height) / (Length of man's shadow) = (Lamppost height) / (Length of lamppost shadow)
1.9 / x = 3.2 / 2.4
4. Solve the proportion: Cross multiply to solve for x:
1.9 * 2.4 = 3.2 * x
4.56 = 3.2x
5. Solve for x: Divide both sides by 3.2 to isolate x:
x = 4.56 / 3.2
x ≈ 1.425
Therefore, the approximate length of the man's shadow is 1.425 meters.