Question

A 28-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 33 m. Find the length of the shadow. If necessary, round your answer to the nearest tenth.

Answer 1

The length of the shadow cast by the building is approximately 17.5 meters when rounded to the nearest tenth, as calculated using the Pythagorean theorem.

Step-by-step explanation:

To find the length of the shadow cast by a 28-m tall building, when the distance from the top of the building to the tip of the shadow is 33 m, we can use the Pythagorean theorem.

This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the building and the shadow form the two legs of a right-angled triangle, and the distance from the top of the building to the tip of the shadow is the hypotenuse.

Let the length of the shadow be x meters.

The Pythagorean theorem can therefore be written as:

28^2 + x^2 = 33^2

Now we solve for x:

1. 28^2 = 784
2. 33^2 = 1089
3. 1089 - 784 = 305
4. x^2 = 305
5. x = √305
6. x ≈ 17.5 m

So, the length of the shadow is approximately 17.5 meters, rounded to the nearest tenth.