Lamppost Lamp
Lamppost Lamp
Can you help me solve this math problem involving proportions (see details)?
Bob is 4 ft. tall and walking away from a vertical lamppost of unknown height. Bob’s shadow from the light on top of the post is increasing 2 times as fast as he is walking away from it. How high is the lamp post?
You don’t have to give me the exact answer (you can if you want), but what I’d really like to know is the steps involved in setting up and solving this problem.
Start off by drawing the scene.
Draw a line representing the ground and on the left draw a line representing the lamppost. Label it as length L.
Now draw a line to the right of the post representing Bob. Label it as length B = 4.
Now draw a line going from the top of the lamppost that touches the top of Bob’s head and goes staight until it hits the ground. This tells you where his shadow ends.
You should now have a couple right triangles. Note that they share an angle. Since the share an angle and one of the other angles is a right angle for both triangles, you can deduce that they are similar triangles.
Since they are similar and you know Bob’s height, you can determine the lamppost height if you know the ratio for the lengths of similar sides.
That’s where the walking and shadow growing part comes in.
Let’s say Bob walked x feet. Label that on your diagram (it’s the segment between the lamppost and Bob).
If he walked x feet, then his shadow must have grown 2x feet. Go ahead and label that on your diagram (it’s the segment between Bob and the shared angle).
So you know the length of one side of the smaller triangle is 2x and the length of the similar side of the larger triangle is 3x (2x + x).
So the ratio is 3:2. Apply that ratio to Bob’s height:
4 * 3 / 2 = 6ft. The lamppost is 6″ tall.
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Tags: lamp, lamppost, lamppost lamp, lamppost lamp post, lamppost lamp post spelling, lamppost or lamp post, outdoor, powered, solar
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