x 32 175 у риу
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
Find X
![### Example Problem: Finding the Length of the Side in a Right-Angled Triangle
**Problem:**
You are given a right-angled triangle with one angle measuring 32 degrees. The side adjacent to this angle is labeled as "15" units long. The side opposite to the 32-degree angle is represented by "x". Your task is to find the value of \(x\).
**Diagram:**
A right-angled triangle is depicted. The triangle includes:
- An angle marked as 32°.
- The side adjacent to the 32° angle is labeled as 15 units.
- The side opposite to the 32° angle is labeled as \(x\).
- The hypotenuse is indicated by the right-angle symbol but is not labeled with a value.
**Steps to Solve:**
1. **Identify the trigonometric function to use**:
Since you have the adjacent side and need to find the opposite side, you can use the tangent function.
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
2. **Substitute the known values**:
\[
\tan(32^\circ) = \frac{x}{15}
\]
3. **Solve for \(x\)**:
\[
x = 15 \times \tan(32^\circ)
\]
4. **Calculate the value**:
Using a calculator to find \(\tan(32^\circ)\):
\[
\tan(32^\circ) \approx 0.6249
\]
Therefore,
\[
x \approx 15 \times 0.6249 = 9.37
\]
**Answer**:
The length of the side opposite the 32-degree angle is approximately 9.37 units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87c6590a-3759-4f4e-bb57-64d6c25bd8a3%2Fe1977adf-83fa-4b24-818b-c521d62c5a07%2Fski03i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem: Finding the Length of the Side in a Right-Angled Triangle
**Problem:**
You are given a right-angled triangle with one angle measuring 32 degrees. The side adjacent to this angle is labeled as "15" units long. The side opposite to the 32-degree angle is represented by "x". Your task is to find the value of \(x\).
**Diagram:**
A right-angled triangle is depicted. The triangle includes:
- An angle marked as 32°.
- The side adjacent to the 32° angle is labeled as 15 units.
- The side opposite to the 32° angle is labeled as \(x\).
- The hypotenuse is indicated by the right-angle symbol but is not labeled with a value.
**Steps to Solve:**
1. **Identify the trigonometric function to use**:
Since you have the adjacent side and need to find the opposite side, you can use the tangent function.
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
2. **Substitute the known values**:
\[
\tan(32^\circ) = \frac{x}{15}
\]
3. **Solve for \(x\)**:
\[
x = 15 \times \tan(32^\circ)
\]
4. **Calculate the value**:
Using a calculator to find \(\tan(32^\circ)\):
\[
\tan(32^\circ) \approx 0.6249
\]
Therefore,
\[
x \approx 15 \times 0.6249 = 9.37
\]
**Answer**:
The length of the side opposite the 32-degree angle is approximately 9.37 units.
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