Given that A = 46° in the picture below, find the length of the two legs. Round your answers to the nearest thousandth. 2 leg adjacent to A = leg opposite to A = Question Help: Message instruct A 9
Given that A = 46° in the picture below, find the length of the two legs. Round your answers to the nearest thousandth. 2 leg adjacent to A = leg opposite to A = Question Help: Message instruct A 9
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
![**Problem Statement:**
Given that \( A = 46^\circ \) in the picture below, find the length of the two legs. Round your answers to the nearest thousandth.
**Diagram:**
The diagram displays a right-angled triangle. The angle \( A \) at the bottom left corner is \( 46^\circ \), which is marked with a blue arc. The triangle has the following known sides:
1. The hypotenuse, opposite the right angle, is labeled as \( 4 \).
2. One of the legs opposite angle \( A \) is labeled as \( 2 \).
3. The other leg, adjacent to angle \( A \), is left unmarked.
**Formulas:**
We will use trigonometric functions to find the unknown lengths:
1. Cosine function: \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\)
2. Sine function: \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\)
Given the known angle (\( A = 46^\circ \)) and the hypotenuse (\( 4 \)), we can find the lengths of the adjacent and opposite legs.
**Solution:**
1. Length of the leg adjacent to \( A \):
\[ \cos(46^\circ) = \frac{\text{adjacent leg}}{4} \]
\[ \text{adjacent leg} = 4 \cdot \cos(46^\circ) \]
2. Length of the leg opposite to \( A \):
\[ \sin(46^\circ) = \frac{\text{opposite leg}}{4} \]
\[ \text{opposite leg} = 4 \cdot \sin(46^\circ) \]
**Input Fields:**
- **Leg adjacent to \( A \) =** [Input box]
- **Leg opposite to \( A \) =** [Input box]
**Support:**
- [Message instructor] (A clickable link or button to get help from the instructor)
**Notes:**
For accuracy, make sure to use a calculator set to degrees when computing the trigonometric functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc1123ec-a0e0-4e35-afe0-df78f47a58b5%2Fd9196cd2-a42b-4040-b13b-bebfe9f517a5%2F5k864mh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given that \( A = 46^\circ \) in the picture below, find the length of the two legs. Round your answers to the nearest thousandth.
**Diagram:**
The diagram displays a right-angled triangle. The angle \( A \) at the bottom left corner is \( 46^\circ \), which is marked with a blue arc. The triangle has the following known sides:
1. The hypotenuse, opposite the right angle, is labeled as \( 4 \).
2. One of the legs opposite angle \( A \) is labeled as \( 2 \).
3. The other leg, adjacent to angle \( A \), is left unmarked.
**Formulas:**
We will use trigonometric functions to find the unknown lengths:
1. Cosine function: \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\)
2. Sine function: \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\)
Given the known angle (\( A = 46^\circ \)) and the hypotenuse (\( 4 \)), we can find the lengths of the adjacent and opposite legs.
**Solution:**
1. Length of the leg adjacent to \( A \):
\[ \cos(46^\circ) = \frac{\text{adjacent leg}}{4} \]
\[ \text{adjacent leg} = 4 \cdot \cos(46^\circ) \]
2. Length of the leg opposite to \( A \):
\[ \sin(46^\circ) = \frac{\text{opposite leg}}{4} \]
\[ \text{opposite leg} = 4 \cdot \sin(46^\circ) \]
**Input Fields:**
- **Leg adjacent to \( A \) =** [Input box]
- **Leg opposite to \( A \) =** [Input box]
**Support:**
- [Message instructor] (A clickable link or button to get help from the instructor)
**Notes:**
For accuracy, make sure to use a calculator set to degrees when computing the trigonometric functions.
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