each time old faithful in Yellowstone national park erupts, rangers can estimate the height of the geyser by comparing it to the height of a tree. first the Rangers locate a tree of the same height . the shadow of the tree is 93 feet at the same time that the shadow of a 6ft ranger is 4ft. Find the height of the tree to the nearest foot. How do I solve this?
6/4 = x/93
Cross multiply and solve for x.
93
To solve this problem, you can use proportions. Here's how:
1. Set up a proportion to relate the height of the tree to its shadow length:
- Let x be the height of the tree.
- The shadow of the tree is 93 feet when the shadow of a 6-foot ranger is 4 feet.
- So, the proportion is: x/93 = 6/4.
2. Cross-multiply and solve for x:
- Cross-multiplying gives you 4x = 6 * 93.
- Simplifying, you get 4x = 558.
- Dividing both sides of the equation by 4 gives you x = 558/4.
- x = 139.5 feet.
Since the height of the tree should be rounded to the nearest foot, the height of the tree is approximately 140 feet.