On a sunny day an office building casts a shadow that is 80 feet long. At the same time, a 5 foot person casts a 6 foot shadow. Determine the height of the office building to the nearest
5/6 = x/80
Cross multiply and solve for x.
3/20
To determine the height of the office building, we can use the concept of similar triangles.
Let's assign variables to the unknowns:
- Height of the office building: h
- Length of the office building's shadow: x
We know that the person's height is 5 feet, and their shadow is 6 feet long. We can set up a proportion using the office building's measurements:
(person's height) / (person's shadow) = (office building's height) / (office building's shadow)
Substituting the known values:
5 feet / 6 feet = h / x
Now, we can solve for x, the length of the office building's shadow:
Cross-multiplying:
5 * x = 6 * h
Simplifying:
5x = 6h
To find the height of the office building, we need to know the length of its shadow. Given that the office building's shadow is 80 feet long:
5 * 80 = 6 * h
400 = 6h
Dividing both sides of the equation by 6:
400 / 6 = h
h ≈ 66.67 feet
Therefore, the height of the office building is approximately 66.67 feet when rounded to the nearest whole number.