At 3:00 PM a man 140 cm tall casts a shadow 147 cm long. At the same time, a tall building nearby casts a shadow 196 m long. How tall is the building?
Well, we do not agree.
147 is not much more than 140
so the height will be almost 196
To determine the height of the building, we can use the concept of similar triangles. Since the man's height and his shadow form a triangle, and the building's height and its shadow form another triangle, we can set up a proportion.
Let's define the variables:
Man's height = h1 = 140 cm
Man's shadow = s1 = 147 cm
Building's height = h2 (unknown)
Building's shadow = s2 = 196 m (note that the unit is different)
To set up the proportion, we can compare the ratios of the corresponding sides of the triangles:
h1 / s1 = h2 / s2
Substituting the given values, we have:
140 / 147 = h2 / 196
Now, we can solve for h2. To do this, cross-multiply and then divide by the known values:
140 * 196 = 147 * h2
h2 = (140 * 196) / 147
Using a calculator, we can evaluate this expression:
h2 ≈ 187.97 cm
Therefore, the height of the building is approximately 187.97 cm.
To find the height of the building, we can set up a proportion using the man's height, the length of his shadow, and the length of the building's shadow.
Let's assign variables to the unknowns: "x" will represent the height of the building.
The proportion can be set up as follows:
(man's height) / (man's shadow length) = (building's height) / (building's shadow length)
Plugging in the given values:
140 cm / 147 cm = x / 196 cm
To solve for x, we can cross-multiply and then divide:
(140 cm * 196 cm) / 147 cm = x
(27440 cm^2) / 147 cm = x
Now we can simplify and solve for x:
187.1 cm ≈ x
Therefore, the height of the building is approximately 187.1 cm.
height/shadow = 140/147 = h/196
so
h = 140 * 196 / 147 = 186.67