if you are 6 ft tall and cast a 90" shadow and are standing 70" from a lamp how tall is the lamp
To determine the height of the lamp, we can use similar triangles and the concept of proportional reasoning.
Here's how you can find the height of the lamp:
Step 1: Identify the two similar triangles involved in the problem. In this case, we have two triangles: one formed by you, your shadow, and the distance from you to the lamp, and another triangle formed by the lamp, its shadow, and its height.
Step 2: Set up a proportion using the corresponding sides of the similar triangles. The height of the lamp will be the variable we are trying to find. Let's call it "h." The proportion can be set up as follows:
(height of you) / (length of your shadow) = (height of the lamp) / (length of the lamp's shadow)
6 ft / 90 in = h / 70 in
Step 3: Solve the proportion for "h" by cross-multiplication:
(6 ft) * (70 in) = (90 in) * h
420 ft*in = 90 in * h
Step 4: Convert the units for easier calculation. Multiply both sides of the equation by 1 ft/12 in to convert inches to feet.
(420 ft*in) * (1 ft / 12 in) = (90 in) * h * (1 ft / 12 in)
35 ft*in = 7.5 ft * h
Step 5: Solve the equation for "h" by dividing both sides by 7.5 ft:
(35 ft*in) / (7.5 ft) = h
4.67 ft = h
Therefore, the height of the lamp is approximately 4.67 feet.