Suppose you are standing such that a 36-foot tree is directly between you and the sun. If you are standing 160 feet away from the tree and the tree casts a 180- foot shadow, how tall could you be and still be completely in the shadow of the tree? X Your height is decimal place.) 160 ft 180 ft ft (If needed, round to 1 36 ft
Suppose you are standing such that a 36-foot tree is directly between you and the sun. If you are standing 160 feet away from the tree and the tree casts a 180- foot shadow, how tall could you be and still be completely in the shadow of the tree? X Your height is decimal place.) 160 ft 180 ft ft (If needed, round to 1 36 ft
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem Statement:**
Suppose you are standing such that a 36-foot tree is directly between you and the sun. If you are standing 160 feet away from the tree and the tree casts a 180-foot shadow, how tall could you be and still be completely in the shadow of the tree?
**Diagram Explanation:**
- The diagram illustrates a right triangle formed by the tree, its shadow, and the line of sight between you and the top of the tree.
- The tree is 36 feet tall.
- The distance from the tree to the end of its shadow is 180 feet.
- You are positioned 160 feet away from the tree within its shadow.
- The height at which you could be completely in the shadow is labeled as \(x\) in the diagram.
**Calculation:**
To find \(x\), use the similar triangles method:
\[ \frac{x}{160} = \frac{36}{180} \]
Solving for \(x\):
1. Cross-multiply: \(180x = 36 \times 160\)
2. Calculate: \(180x = 5760\)
3. Divide both sides by 180: \(x = \frac{5760}{180}\)
4. Simplify: \(x = 32\)
So, Your height is \(32\) ft.
(If needed, round to 1 decimal place.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ec86780-754e-4dc1-88b7-062788875a29%2Fdc993ce1-3b82-482e-9224-6c3f2e523884%2Fd34s4sh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Suppose you are standing such that a 36-foot tree is directly between you and the sun. If you are standing 160 feet away from the tree and the tree casts a 180-foot shadow, how tall could you be and still be completely in the shadow of the tree?
**Diagram Explanation:**
- The diagram illustrates a right triangle formed by the tree, its shadow, and the line of sight between you and the top of the tree.
- The tree is 36 feet tall.
- The distance from the tree to the end of its shadow is 180 feet.
- You are positioned 160 feet away from the tree within its shadow.
- The height at which you could be completely in the shadow is labeled as \(x\) in the diagram.
**Calculation:**
To find \(x\), use the similar triangles method:
\[ \frac{x}{160} = \frac{36}{180} \]
Solving for \(x\):
1. Cross-multiply: \(180x = 36 \times 160\)
2. Calculate: \(180x = 5760\)
3. Divide both sides by 180: \(x = \frac{5760}{180}\)
4. Simplify: \(x = 32\)
So, Your height is \(32\) ft.
(If needed, round to 1 decimal place.)
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