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
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
100%
![**Problem Statement:**
In ΔTUV, the measure of ∠V = 90°, the measure of ∠U = 48°, and VT = 88 feet. Find the length of UV to the nearest tenth of a foot.
**Graph:**
A right triangle ΔTUV is depicted with the following details:
- ∠V is 90 degrees, making it a right angle.
- ∠U is 48 degrees.
- UV is marked as the side opposite to ∠U.
- VT is 88 feet, which is the side adjacent to ∠U.
- TU is the hypotenuse of the triangle.
To solve the problem and find the length of UV, we can use trigonometric functions. The tangent function is particularly useful here because it relates the opposite side to the adjacent side in a right triangle.
### Calculation:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Where:
\[ \theta = 48^\circ \]
\[ \text{opposite} = UV \]
\[ \text{adjacent} = VT = 88 \]
Therefore,
\[ \tan(48^\circ) = \frac{UV}{88} \]
\[ UV = 88 \times \tan(48^\circ) \]
Using a calculator,
\[ \tan(48^\circ) \approx 1.1106 \]
So,
\[ UV \approx 88 \times 1.1106 \]
\[ UV \approx 97.8 \]
Thus, the length of UV to the nearest tenth of a foot is:
\[ \boxed{97.8 \text{ feet}} \]
Please enter your answer in the box provided and click "Submit Answer".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c4733b3-62a7-4130-97e7-e603f16978d9%2Ffab7d415-c828-46f9-a4c8-7e999080c1f1%2Fkf7j3l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
In ΔTUV, the measure of ∠V = 90°, the measure of ∠U = 48°, and VT = 88 feet. Find the length of UV to the nearest tenth of a foot.
**Graph:**
A right triangle ΔTUV is depicted with the following details:
- ∠V is 90 degrees, making it a right angle.
- ∠U is 48 degrees.
- UV is marked as the side opposite to ∠U.
- VT is 88 feet, which is the side adjacent to ∠U.
- TU is the hypotenuse of the triangle.
To solve the problem and find the length of UV, we can use trigonometric functions. The tangent function is particularly useful here because it relates the opposite side to the adjacent side in a right triangle.
### Calculation:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Where:
\[ \theta = 48^\circ \]
\[ \text{opposite} = UV \]
\[ \text{adjacent} = VT = 88 \]
Therefore,
\[ \tan(48^\circ) = \frac{UV}{88} \]
\[ UV = 88 \times \tan(48^\circ) \]
Using a calculator,
\[ \tan(48^\circ) \approx 1.1106 \]
So,
\[ UV \approx 88 \times 1.1106 \]
\[ UV \approx 97.8 \]
Thus, the length of UV to the nearest tenth of a foot is:
\[ \boxed{97.8 \text{ feet}} \]
Please enter your answer in the box provided and click "Submit Answer".
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning