Lamppost Lamp
Can you help me solve this math problem involving proportions (see details)?
Bob is 4 m. height and walk a streetlight vertical height unknown. Bob's shadow from the light on top of the post is always 2 times as fast as he moves away from it. How tall is the lamppost? You I must give the correct answer (you can if you wish), but what I'd like to know the steps involved in setting up and solving this problem.
Starting from the design stage. Draw a line on the left represents the land and draw a line that represents the lamp. Label as length L. Now draw a line to the right of place that represents Bob. Label as length B = 4. Now draw a line going from the top of the lamp that touches the top of the head of Bob and go staight until it touches land. This tells you where it ends its shadow. You should now have a couple right triangles. Note that share a corner. Since the share of a corner and one of the other angles is a right angle to both triangles, we can deduce that they are similar triangles. Since they are similar and we know the height of Bob, you can determine the height of streetlight if you know the ratio for the length of the sides similar. That's where the shadow walking and growing part comes in. Let's say Bob walked x feet. Label diagram (this is the segment between the streetlight and Bob). If you've walked x feet, then its shadow must have grown 2x feet. Go ahead and that the label on the diagram (it the segment between Bob and the corner in common). So you know the length of one side of the smaller triangle is 2x and the length of the side similar to the larger triangle is 3x (2x + x). So the ratio is 3:2. Applying this ratio to Bob at: 4 * 3 / 2 = 6 feet. The lamp is 6 "tall.
Leaning on a Lamp Post
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