Homework Help is Here – Start Your Trial Now!
Math
Geometry
? 38 27

? 38 27

Elementary Geometry For College Students, 7e
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
See similar textbooks
icon
Related questions
Question

See picture 

In the provided image, we have a right triangle. Here's a detailed explanation and transcription of the elements of the diagram: ### Diagram Explanation: - The triangle is a right triangle, indicated by a small square at the angle. - The length of the horizontal leg (base) of the triangle is labeled as 38. - The length of the vertical leg (height) of the triangle is labeled as 27. - The hypotenuse (the side opposite the right angle) is not labeled with a length, but the angle adjacent to the base and the hypotenuse is marked with a question mark (?), indicating that this is the angle we need to find. ### Steps to Find the Missing Angle: 1. **Identify the Known Elements:** - Base (adjacent side) = 38 - Height (opposite side) = 27 2. **Use Trigonometric Ratios:** - Since we need to find the angle, we can use the tangent function, which is the ratio of the opposite side to the adjacent side. \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] \[ \tan(\theta) = \frac{27}{38} \] 3. **Calculate the Angle:** - Use the arctangent function (tan^(-1)) to find the angle. \[ \theta = \tan^{-1}\left(\frac{27}{38}\right) \] - Calculate this value using a calculator or trigonometric tables. By performing the calculation, students will find the value of the angle marked with the question mark. This method demonstrates practical usage of trigonometric functions in solving right triangle problems.
Transcribed Image Text:In the provided image, we have a right triangle. Here's a detailed explanation and transcription of the elements of the diagram: ### Diagram Explanation: - The triangle is a right triangle, indicated by a small square at the angle. - The length of the horizontal leg (base) of the triangle is labeled as 38. - The length of the vertical leg (height) of the triangle is labeled as 27. - The hypotenuse (the side opposite the right angle) is not labeled with a length, but the angle adjacent to the base and the hypotenuse is marked with a question mark (?), indicating that this is the angle we need to find. ### Steps to Find the Missing Angle: 1. **Identify the Known Elements:** - Base (adjacent side) = 38 - Height (opposite side) = 27 2. **Use Trigonometric Ratios:** - Since we need to find the angle, we can use the tangent function, which is the ratio of the opposite side to the adjacent side. \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] \[ \tan(\theta) = \frac{27}{38} \] 3. **Calculate the Angle:** - Use the arctangent function (tan^(-1)) to find the angle. \[ \theta = \tan^{-1}\left(\frac{27}{38}\right) \] - Calculate this value using a calculator or trigonometric tables. By performing the calculation, students will find the value of the angle marked with the question mark. This method demonstrates practical usage of trigonometric functions in solving right triangle problems.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS