Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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estimate how tall the tree is

![Title: Analyzing the Height of a Tree Using Trigonometry
**Diagram Description:**
This diagram represents a right triangle used to calculate the height of a tree using trigonometric principles. It includes the following components:
1. **Angle of Elevation**: The angle between the horizontal line (ground) and the line of sight to the top of the tree is labeled as 45 degrees.
2. **Distance from Tree**: The horizontal side of the triangle, representing the distance from the observer to the base of the tree, is marked as 120 feet.
3. **Height of the Tree (h)**: The vertical side of the triangle, from the base to the top of the tree, is labeled with "h," representing the height of the tree which needs to be calculated.
**Mathematical Explanation:**
Using the tangent function in trigonometry, where:
\[ \tan(\theta) = \frac{\text{Opposite Side}}{\text{Adjacent Side}} \]
Here, \(\theta\) is 45 degrees, the opposite side is the height of the tree (h), and the adjacent side is 120 feet.
Since \(\tan(45^\circ) = 1\), we have:
\[ 1 = \frac{h}{120} \]
Solving for \(h\), we get:
\[ h = 120 \text{ feet} \]
This demonstrates how a simple trigonometric ratio can be used to find the height of an object when its distance and angle of elevation are known.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7dd02ea2-2714-402e-9b7e-8c1ff6026f64%2Feaf4dce6-7c9a-46f2-9819-ad3e24d4031a%2Fo6rcfep_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Analyzing the Height of a Tree Using Trigonometry
**Diagram Description:**
This diagram represents a right triangle used to calculate the height of a tree using trigonometric principles. It includes the following components:
1. **Angle of Elevation**: The angle between the horizontal line (ground) and the line of sight to the top of the tree is labeled as 45 degrees.
2. **Distance from Tree**: The horizontal side of the triangle, representing the distance from the observer to the base of the tree, is marked as 120 feet.
3. **Height of the Tree (h)**: The vertical side of the triangle, from the base to the top of the tree, is labeled with "h," representing the height of the tree which needs to be calculated.
**Mathematical Explanation:**
Using the tangent function in trigonometry, where:
\[ \tan(\theta) = \frac{\text{Opposite Side}}{\text{Adjacent Side}} \]
Here, \(\theta\) is 45 degrees, the opposite side is the height of the tree (h), and the adjacent side is 120 feet.
Since \(\tan(45^\circ) = 1\), we have:
\[ 1 = \frac{h}{120} \]
Solving for \(h\), we get:
\[ h = 120 \text{ feet} \]
This demonstrates how a simple trigonometric ratio can be used to find the height of an object when its distance and angle of elevation are known.
Expert Solution
Step 1
We have to find the height of the tree.
We will use trigonometric ratios here.
Step by step
Solved in 2 steps with 1 images
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