A woman wants to measure the height of the building. She places a 7 ft pole in the shadow of the building s I that the shadow of the building. The total length of the building is 167 ft, and the pole casts a shadow the is 5.5 ft long. How tall is the building?
assuming you meant the total length of the building's shadow is 167 ft,
h/167 = 7/5.5
To find the height of the building, we can use similar triangles. The ratio of the length of the pole's shadow to the length of the pole is equal to the ratio of the length of the building's shadow to the height of the building.
Let's denote the height of the building as 'h'.
We are given the following information:
Length of the pole: 7 ft
Length of the pole's shadow: 5.5 ft
Length of the building: 167 ft
Using the ratio of the lengths of the shadows, we can set up the equation:
5.5 ft / 7 ft = (Length of the building's shadow) / h
Let's solve for the height of the building 'h':
5.5 ft = (167 ft) / h
Cross-multiplying, we get:
5.5 ft * h = 167 ft
Dividing both sides of the equation by 5.5, we have:
h = 167 ft / 5.5 ft
Calculating this, we find:
h ≈ 30.36 ft
Therefore, the height of the building is approximately 30.36 ft.
To determine the height of the building, we can set up a proportion using the similar triangles formed by the pole and its shadow, and the building and its shadow.
Let's assume "x" represents the height of the building.
Using the given information:
Height of pole = 7 ft
Length of pole's shadow = 5.5 ft
Length of building = 167 ft
We can create the following proportion:
Height of building / Length of building = Height of pole / Length of pole's shadow
Substituting the values:
x / 167 = 7 / 5.5
To solve for x, we can cross-multiply and then divide:
5.5x = 7 * 167
Multiply 7 by 167:
5.5x = 1169
Divide both sides by 5.5:
x = 1169 / 5.5
Evaluating the division:
x ≈ 212.545
Hence, the height of the building is approximately 212.545 feet.