a boy stands 1 meter away from a lamppost. he is 1.8 meters tall and casts a shadow 2 meters long in the light from the lamp. how tall is the lamppost?

2.7

To find the height of the lamppost, we can use similar triangles. Let's define the variables:

h = height of the lamppost (what we want to find)
d = distance between the boy and the lamppost (given as 1 meter)
B = height of the boy (given as 1.8 meters)
b = length of the boy's shadow (given as 2 meters)

We can set up the following proportion between the two similar triangles formed by the lamppost and the boy:

h/B = (h + d)/b

Let's solve for h by cross-multiplying:

b(h + d) = B(h)

Expanding the equation:

2(h + 1) = 1.8h

Simplifying:

2h + 2 = 1.8h

Subtracting 1.8h from both sides:

0.2h + 2 = 0

Subtracting 2 from both sides:

0.2h = -2

Dividing both sides by 0.2 to isolate h:

h = -2 / 0.2

Solving:

h = -10

Since a negative height doesn't make sense in this context, it seems there may have been an error in the calculations or information provided. Please double-check the values given to ensure accuracy.

To find the height of the lamppost, we can use similar triangles. Let's understand the concept and steps to solve this problem:

1. Draw a diagram: Sketch a diagram representing a boy standing next to the lamppost with the given measurements. Label the values that are provided in the problem.

2. Identify similar triangles: In this situation, we have two similar triangles - the triangle formed by the boy, his shadow, and the lamppost, and the triangle formed by the lamppost, its shadow, and the ground.

3. Set up a proportion: Since the triangles are similar, the ratio of the corresponding sides will be equal. Let's represent the height of the lamppost as 'x'. The proportion can be set up as follows:

(Height of the lamppost) / (Length of the boy's shadow) = (Height of the boy) / (Length of the boy's shadow)

x / 2 = 1.8 / 1

4. Solve for x: To find the height of the lamppost, we can cross-multiply and solve for x:

x = (1.8 * 2) / 1

x = 3.6 meters

Therefore, the lamppost is 3.6 meters tall.

with appropriate labels,

1.8/2 = h/(1+2)