Use Figure 1 to evaluate the trigonometric function. Enter the exact answer. tan A 16 6 √a al k B sin (a) 14 Figure 1 E 6 125
Use Figure 1 to evaluate the trigonometric function. Enter the exact answer. tan A 16 6 √a al k B sin (a) 14 Figure 1 E 6 125
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°.
Related questions
Question
(Note: Insert an image similar to Figure 1 above)
---
**Figure 1** shows a right-angle triangle with the following measurements:
- Length of side \( AB \) (adjacent to angle \( A \)): 14 units
- Length of side \( AC \) (opposite to angle \( A \)): 6 units
The goal is to determine the exact value of \( \tan A \).
#### Solution:
To calculate \( \tan A \), we use the trigonometric definition:
\[ \tan A = \frac{\text{opposite}}{\text{adjacent}} \]
For Figure 1:
- The opposite side to angle \( A \) is \( AC \) with length 6 units.
- The adjacent side to angle \( A \) is \( AB \) with length 14 units.
Therefore,
\[ \tan A = \frac{6}{14} = \frac{3}{7} \]
Thus, the exact value of \( \tan A \) is:
\[ \boxed{\frac{3}{7}} \]
---
#### Enter the exact answer:
Below the provided question, an answer box is shown where users can input their solutions. The interface includes buttons for entering mathematical expressions like exponents, fractions, square roots, absolute values, and common trigonometric functions (e.g., sin(θ), π).
In this specific example:
\[ \text{tan } A = \frac{3}{7} \]
---
This problem exemplifies the process of evaluating basic trigonometric functions using a right-angle triangle. Understanding these concepts is crucial for solving various types of geometry and trigonometry problems.
For more educational content and practice problems, continue exploring our website.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2da59d05-ea7a-47ad-8289-54dec09680e5%2F69131306-2731-40ef-91eb-bfaff58112e5%2F7qnhg18_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem: Evaluating Trigonometric Functions
#### Question:
Use **Figure 1** to evaluate the trigonometric function.
(Note: Insert an image similar to Figure 1 above)
---
**Figure 1** shows a right-angle triangle with the following measurements:
- Length of side \( AB \) (adjacent to angle \( A \)): 14 units
- Length of side \( AC \) (opposite to angle \( A \)): 6 units
The goal is to determine the exact value of \( \tan A \).
#### Solution:
To calculate \( \tan A \), we use the trigonometric definition:
\[ \tan A = \frac{\text{opposite}}{\text{adjacent}} \]
For Figure 1:
- The opposite side to angle \( A \) is \( AC \) with length 6 units.
- The adjacent side to angle \( A \) is \( AB \) with length 14 units.
Therefore,
\[ \tan A = \frac{6}{14} = \frac{3}{7} \]
Thus, the exact value of \( \tan A \) is:
\[ \boxed{\frac{3}{7}} \]
---
#### Enter the exact answer:
Below the provided question, an answer box is shown where users can input their solutions. The interface includes buttons for entering mathematical expressions like exponents, fractions, square roots, absolute values, and common trigonometric functions (e.g., sin(θ), π).
In this specific example:
\[ \text{tan } A = \frac{3}{7} \]
---
This problem exemplifies the process of evaluating basic trigonometric functions using a right-angle triangle. Understanding these concepts is crucial for solving various types of geometry and trigonometry problems.
For more educational content and practice problems, continue exploring our website.
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