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?
Now Sabrina,
We did the previous problem for you. It is very similar to this problem. Please try it. It is really just trig.
is it
D/5.8= 1.2/2.8
D= (5.8x1.2)/2.8
D= 2.48m
??
can someone help? i am really struggling
could i have a clue or a starting point please?
2.8/(3+x) = 1.2/x,
2.8• x =1.2•3+1.2•x,
x=3.6/1.6=2.25 m
To find the length of the shadow cast by the child upon the ground, we can use similar triangles.
Let's label the height of the child as 'h', the height of the lamp post as 'H', and the length of the shadow as 's'.
According to the given information, the child's height is 1.2 meters, and the height of the lamp post is 2.8 meters.
Since the lamp post and the shadow form two similar triangles, we can set up the following proportion:
h / H = s / (s + 3)
Substituting the given values:
1.2 / 2.8 = s / (s + 3)
Cross-multiplying and simplifying:
1.2(s + 3) = 2.8s
1.2s + 3.6 = 2.8s
3.6 = 2.8s - 1.2s
3.6 = 1.6s
Dividing both sides by 1.6:
s = 3.6 / 1.6 = 2.25
Therefore, the length of the shadow cast by the child upon the ground is 2.25 meters.