Need help.....
A child of height 1.2 metres stands 3 metres from the foot of a lamp post of height 2.8 metres, at the top of which there is a small source which can be considered as a point. What is the length of the shadow cast by the child upon the ground?
make a sketch
let the length of the child's shadow be x m
from the similar triangles....
1.2/x = 2.8/(x+3)
2.8x = 1.2x + 3.6
1.6x = 3.6
x = 2.25
thanks for your help
To find the length of the shadow cast by the child, we can use similar triangles.
First, let's label the given information:
Height of the child (h1) = 1.2 meters
Distance of the child from the lamp post (d1) = 3 meters
Height of the lamp post (h2) = 2.8 meters
Now, we can set up a proportion based on the similar triangles formed by the child, the lamp post, and their respective shadows.
The proportion is as follows:
(h1 + length of the shadow of the child) / length of the shadow of the lamp post = h1 / h2
Let's plug in the given values and solve for the length of the shadow of the child:
(1.2 + shadow length) / length of the shadow of the lamp post = 1.2 / 2.8
Cross-multiplying, we get:
1.2 + shadow length = (1.2 / 2.8) * length of the shadow of the lamp post
Next, isolate the shadow length by subtracting 1.2 from both sides:
shadow length = (1.2 / 2.8) * length of the shadow of the lamp post - 1.2
Now, we need to find the length of the shadow of the lamp post. Since we are dealing with similar triangles, we can use the concept of proportions to calculate it.
We know the corresponding sides are proportional:
length of the shadow of the lamp post / distance of the lamp post from the child = h2 / h1
Plugging in the given values:
length of the shadow of the lamp post / 3 = 2.8 / 1.2
Simplifying, we get:
length of the shadow of the lamp post = (2.8 / 1.2) * 3
Now that we have the length of the shadow of the lamp post, we can plug it back into the previous equation to calculate the shadow length of the child:
shadow length = (1.2 / 2.8) * [(2.8 / 1.2) * 3] - 1.2
Calculating this expression will give us the length of the shadow cast by the child upon the ground.