Suppose the space needle in seattle washington casts a 220 ft shadow at the same time a nearby tourist cast a 2- foot shadow if the tourist is 5.5 feet tall how tall is the space needle
To determine the height of the Space Needle, we can use the concept of similar triangles. The two shadows, one from the Space Needle and one from the tourist, can be considered as the corresponding sides of two similar triangles.
Let's denote the height of the Space Needle as "x". According to the information given, the height of the tourist is 5.5 feet, and the length of their shadow is 2 feet.
We can set up the following proportion:
Height of the Space Needle / Length of Space Needle's Shadow = Height of the Tourist / Length of Tourist's Shadow
x / 220 = 5.5 / 2
Now, we can solve for "x".
x = (220 * 5.5) / 2
x = 1210 / 2
x = 605
Therefore, the height of the Space Needle is approximately 605 feet.
To calculate the height of the Space Needle, we can use the concept of similar triangles. Here's how you can find the height of the Space Needle:
1. Identify the similar triangles: In this scenario, we have two triangles - the shadow triangle and the height triangle. The Space Needle's height corresponds to the height triangle, while the tourist's height corresponds to the shadow triangle.
2. Set up the proportion: The corresponding sides of similar triangles are in proportion to each other. We can set up the following equation:
(height of Space Needle) / (height of tourist) = (length of Space Needle's shadow) / (length of tourist's shadow)
Plugging in the given values:
(height of Space Needle) / 5.5ft = 220ft / 2ft
3. Solve the proportion for the height of the Space Needle:
Cross-multiplying the equation, we get:
(height of Space Needle) = (220ft / 2ft) * 5.5ft.
Simplifying:
(height of Space Needle) = 110ft * 5.5ft
= 605ft.
Therefore, the Space Needle's height is approximately 605 feet.
Use a proportion. Cross multiply and solve for x.
x/220 = 5.5/2