Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
how would you do 17?
![**Find the Missing Side of a Right Triangle**
Welcome to the Trigonometry section of our Educational website. Today, we are going to solve a classic problem involving a right triangle. Below is a step-by-step explanation to find the missing side of a given right triangle using trigonometric principles.
### Problem Statement:
Find the missing side. Round to the nearest tenth.
```
17)
|\
| \
x | \
| \ 15°
| \
|_____\
25
```
### Given:
- Angle: 15°
- Adjacent side (base): 25 units
- Hypotenuse: x (missing side)
### Choices:
A) 6.7
B) 49.1
C) 93.3
D) 49.4
### Solution:
To find the missing side (hypotenuse, x) in the right triangle, we will use the cosine trigonometric function since the adjacent side (25 units) and the angle (15°) are given.
**Cosine Function:**
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Using this function:
\[ \cos(15°) = \frac{25}{x} \]
Rearrange the equation to solve for x:
\[ x = \frac{25}{\cos(15°)} \]
Using a calculator:
\[ \cos(15°) \approx 0.9659 \]
\[ x = \frac{25}{0.9659} \approx 25.87 \]
Rounding to the nearest tenth:
\[ x \approx 25.9 \]
So, the correct answer should be rounded according to the available choices. The correct, rounded value is:
\[ B) 49.1 \]
However, since "25.9" is not an option, you might want to check for errors either in the question or the calculation. This discrepancy needs to be addressed by reviewing the problem context or the provided answer choices.
**Note:** Ensure the problem boils down to the right calculation and choices available match logically. Consult additional resources or an instructor if you encounter such inconsistencies.
### Visual Explanation:
The illustration displays a right triangle with one angle marked as 15°. The base (adjacent side to this angle) is labeled 25, while we are supposed to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c3597d8-30c2-4840-bf6e-c951942ae65e%2F77c76e5d-1e69-46f8-89ac-b03f5b369768%2Fjb29tsa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the Missing Side of a Right Triangle**
Welcome to the Trigonometry section of our Educational website. Today, we are going to solve a classic problem involving a right triangle. Below is a step-by-step explanation to find the missing side of a given right triangle using trigonometric principles.
### Problem Statement:
Find the missing side. Round to the nearest tenth.
```
17)
|\
| \
x | \
| \ 15°
| \
|_____\
25
```
### Given:
- Angle: 15°
- Adjacent side (base): 25 units
- Hypotenuse: x (missing side)
### Choices:
A) 6.7
B) 49.1
C) 93.3
D) 49.4
### Solution:
To find the missing side (hypotenuse, x) in the right triangle, we will use the cosine trigonometric function since the adjacent side (25 units) and the angle (15°) are given.
**Cosine Function:**
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Using this function:
\[ \cos(15°) = \frac{25}{x} \]
Rearrange the equation to solve for x:
\[ x = \frac{25}{\cos(15°)} \]
Using a calculator:
\[ \cos(15°) \approx 0.9659 \]
\[ x = \frac{25}{0.9659} \approx 25.87 \]
Rounding to the nearest tenth:
\[ x \approx 25.9 \]
So, the correct answer should be rounded according to the available choices. The correct, rounded value is:
\[ B) 49.1 \]
However, since "25.9" is not an option, you might want to check for errors either in the question or the calculation. This discrepancy needs to be addressed by reviewing the problem context or the provided answer choices.
**Note:** Ensure the problem boils down to the right calculation and choices available match logically. Consult additional resources or an instructor if you encounter such inconsistencies.
### Visual Explanation:
The illustration displays a right triangle with one angle marked as 15°. The base (adjacent side to this angle) is labeled 25, while we are supposed to
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