5. Find AB ?
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![The image shows a hand-drawn triangle with geometric notations. Here is a detailed transcription and description suitable for an educational website:
---
## Geometric Problem: Finding the Length of AB
### Diagram Explanation
A right-angled triangle \( \triangle ABC \) is depicted on the paper, with the right angle at \( C \). The triangle includes an internal segment \( CD \), forming smaller right-angled triangles within \( \triangle ABC \).
**Labels and Measurements:**
- Point \( A \) is the leftmost point.
- Point \( B \) is the topmost point.
- Point \( C \) is on the bottom right, forming a right angle (\( \angle ACB \)).
- Point \( D \) lies on line \( AC \), forming a right angle with \( BC \).
**Measurements:**
- \( AC = 6 \, \text{units} \)
- \( CD = 3 \, \text{units} \)
- \( BC = 3 \, \text{units} \)
- \( AD = 5 \, \text{units} \)
### Problem Statement:
Find the length of \( AB \).
### Diagram:
Here’s how the visual representation is structured:
```
B
/|
/ |
5 / | ?
/ | 3
/ |
A----D---C
6
```
### Solution Approach:
To find the length of \( AB \), which is the hypotenuse of the right-angled triangle \( \triangle ABC \), apply the Pythagorean theorem:
\[ AB^2 = AC^2 + BC^2 \]
Given:
- \( AC = 6 \, \text{units} \)
- \( BC = 3 \, \text{units} \)
Calculate \( AB \):
\[ AB^2 = 6^2 + 3^2 \]
\[ AB^2 = 36 + 9 \]
\[ AB^2 = 45 \]
\[ AB = \sqrt{45} \]
\[ AB = 3\sqrt{5} \]
Thus, the length of \( AB \) is \( 3\sqrt{5} \, \text{units} \).
---
This explanation is structured to aid students in understanding the geometric approach to solving the length of \( AB \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb497b8c4-4d07-4c4c-ac55-469da516b240%2Ffde2cae0-0e78-48ba-9a3e-354c109c9aec%2Fo9n9ced_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows a hand-drawn triangle with geometric notations. Here is a detailed transcription and description suitable for an educational website:
---
## Geometric Problem: Finding the Length of AB
### Diagram Explanation
A right-angled triangle \( \triangle ABC \) is depicted on the paper, with the right angle at \( C \). The triangle includes an internal segment \( CD \), forming smaller right-angled triangles within \( \triangle ABC \).
**Labels and Measurements:**
- Point \( A \) is the leftmost point.
- Point \( B \) is the topmost point.
- Point \( C \) is on the bottom right, forming a right angle (\( \angle ACB \)).
- Point \( D \) lies on line \( AC \), forming a right angle with \( BC \).
**Measurements:**
- \( AC = 6 \, \text{units} \)
- \( CD = 3 \, \text{units} \)
- \( BC = 3 \, \text{units} \)
- \( AD = 5 \, \text{units} \)
### Problem Statement:
Find the length of \( AB \).
### Diagram:
Here’s how the visual representation is structured:
```
B
/|
/ |
5 / | ?
/ | 3
/ |
A----D---C
6
```
### Solution Approach:
To find the length of \( AB \), which is the hypotenuse of the right-angled triangle \( \triangle ABC \), apply the Pythagorean theorem:
\[ AB^2 = AC^2 + BC^2 \]
Given:
- \( AC = 6 \, \text{units} \)
- \( BC = 3 \, \text{units} \)
Calculate \( AB \):
\[ AB^2 = 6^2 + 3^2 \]
\[ AB^2 = 36 + 9 \]
\[ AB^2 = 45 \]
\[ AB = \sqrt{45} \]
\[ AB = 3\sqrt{5} \]
Thus, the length of \( AB \) is \( 3\sqrt{5} \, \text{units} \).
---
This explanation is structured to aid students in understanding the geometric approach to solving the length of \( AB \).
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