if you are 6 ft tall and cast a 90" shadow and are standing 70" from a lamp how tall is the lamp
since 6' = 72 inches, if the lamp is x inches tall,
x/(70+90) = 72/90
x = 128
can you further explain the part where you stated...
x/(70+90)=72/90
when I take 72/90 I get .8
I must be missing something here...
draw a diagram. Two ratios are the same
lamp height:distance to shadow tip
person height:length of shadow
so,
x/160 = .8
x = 128
To find the height of the lamp, we can use similar triangles. Here's how we can calculate it step by step:
1. Start by creating a proportion using the height of the person, the length of their shadow, and the distance from the person to the lamp.
Let x be the height of the lamp.
The proportion can be set up as: (height of the person)/(length of shadow) = (height of the lamp)/(distance from the person to the lamp)
Plugging in the values we have:
(6 ft) / (90 in) = x / (70 in)
2. Convert the measurements to the same unit for easier calculation. Since all measurements are currently in different units, let's convert them to inches.
6 ft = 6 ft * 12 in/ft = 72 in
90 in stays the same
70 in stays the same
3. Plug in the converted values into the proportion:
(72 in) / (90 in) = x / (70 in)
4. Solve for x, the height of the lamp.
(72 in) * (70 in) = (90 in) * x
5040 in^2 = 90 in * x
To isolate x, divide both sides of the equation by 90 in:
5040 in^2 / 90 in = x
56 in = x
Therefore, the height of the lamp is 56 inches.