marcel is standing 5 meters away from a street light. he is 2 meters tall and the light is 6 meters high. how long is marcel's shadow?
I am sure you made a sketch.
Let the length of his shadow be x
By similar triangles.....
x/2 = (x+5)/6
6x = 2x+10
carry on
My module
To find the length of Marcel's shadow, we can use similar triangles and proportions.
1. Draw a diagram: Draw a vertical line to represent the street light, and label it as the height of the street light (6 meters). From the bottom of the street light, draw a line representing Marcel's height (2 meters). From the top of Marcel's head, draw a line towards the street light, representing his shadow.
2. Identify the similar triangles: The triangle formed by the street light, Marcel's height, and his shadow is similar to the triangle formed by the street light, Marcel's shadow, and the ground.
3. Set up a proportion: Since the triangles are similar, we can set up a proportion using the corresponding sides of the triangles. Let x represent the length of Marcel's shadow:
(Length of Marcel's shadow) / (Marcel's height) = (Height of the street light) / (Distance between Marcel and the street light)
x / 2 = 6 / 5
4. Solve the proportion: Cross multiply and solve for x:
5x = 2 * 6
5x = 12
x = 12 / 5
Therefore, the length of Marcel's shadow is 2.4 meters.
To find the length of Marcel's shadow, we can use the concept of similar triangles. Similar triangles have the same shape but not necessarily the same size.
In this case, we have two similar right triangles: one formed by Marcel, his shadow, and the ground, and the other formed by the street light, its shadow, and the ground.
The ratio of corresponding sides in similar triangles is equal. Therefore, we can set up the following proportion:
height of Marcel / length of shadow = height of street light / length of street light's shadow
Let's plug in the known values:
2 meters / length of shadow = 6 meters / length of street light's shadow
Now, we can solve for the length of Marcel's shadow by rearranging the equation:
length of shadow = (2 meters * length of street light's shadow) / 6 meters
Given that the length of street light's shadow is equal to the distance from Marcel to the street light plus the height of the street light, we can substitute this value into the equation:
length of shadow = (2 meters * (5 meters + 6 meters)) / 6 meters
Simplifying, we have:
length of shadow = (2 meters * 11 meters) / 6 meters
= 22 meters / 6 meters
≈ 3.67 meters
Therefore, Marcel's shadow is approximately 3.67 meters long.