A tower 25 meters tall casts a shadow 20.8 meters long. What is the distance from the top of the tower to the end of the shadow?
the distance is the hypotenuse of the right triangle ... use Pythagoras
To find the distance from the top of the tower to the end of the shadow, we can use similar triangles. Here's how to get the answer:
1. Draw a diagram: Start by drawing a vertical line to represent the tower. Label it as 25 meters (the height of the tower). Then draw a horizontal line to represent the shadow, labeling it as 20.8 meters (the length of the shadow).
2. Identify the triangles: In this diagram, we have two similar right triangles. One triangle is formed by the height of the tower and its shadow. The other triangle is formed by the distance from the top of the tower to the end of the shadow and the length of the shadow.
3. Set up a proportion: Since the triangles are similar, the ratio of the corresponding sides will be the same. We can set up the following proportion:
height of the tower / length of the shadow = distance from the top of the tower to the end of the shadow / length of the shadow
This can be written as:
25 / 20.8 = x / 20.8
Here, 'x' represents the distance from the top of the tower to the end of the shadow, which is what we want to find.
4. Solve the proportion: Now we can solve the proportion for 'x'. Cross-multiply and divide:
25 * 20.8 = x * 20.8
x = (25 * 20.8) / 20.8
The length of the shadow cancels out, leaving us with:
x = 25 meters
So, the distance from the top of the tower to the end of the shadow is 25 meters.