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Math  /  Geometry

QuestionA pole that is 2.8 m tall casts a shadow that is 1.38 m long. At the same time, a nearby building casts a shadow that is 44.5 m long. How tall is the building? Round your answer to the nearest meter. m Start over

Studdy Solution

STEP 1

1. The pole and the building are both vertical and cast shadows on a flat surface.
2. The sun's rays are parallel, creating similar triangles between the pole and its shadow, and the building and its shadow.

STEP 2

1. Understand the concept of similar triangles.
2. Set up a proportion using the similar triangles.
3. Solve for the height of the building.
4. Round the answer to the nearest meter.

STEP 3

Understand that the problem involves similar triangles. The ratio of the height of the pole to the length of its shadow is the same as the ratio of the height of the building to the length of its shadow.

STEP 4

Set up the proportion using the heights and shadow lengths:
Height of PoleLength of Pole’s Shadow=Height of BuildingLength of Building’s Shadow\frac{\text{Height of Pole}}{\text{Length of Pole's Shadow}} = \frac{\text{Height of Building}}{\text{Length of Building's Shadow}}
Substitute the known values:
2.8 m1.38 m=h44.5 m\frac{2.8 \text{ m}}{1.38 \text{ m}} = \frac{h}{44.5 \text{ m}}

STEP 5

Solve for the height of the building (h h ):
First, calculate the ratio:
2.81.38≈2.028985507\frac{2.8}{1.38} \approx 2.028985507
Now, solve for h h :
h=2.028985507×44.5h = 2.028985507 \times 44.5
Calculate h h :
h≈90.2884058h \approx 90.2884058

STEP 6

Round the height of the building to the nearest meter:
h≈90 mh \approx 90 \text{ m}
The height of the building is approximately:
90 m \boxed{90 \text{ m}}

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