1 Variables, Expressions, And Integers 2 Solving Equations 3 Multi-step Equations And Inequalities 4 Factors, Fractions, And Exponents 5 Rational Numbers And Equations 6 Ratio, Proportion, And Probability 7 Percents 8 Linear Functions 9 Real Numbers And Right Triangles 10 Measurement, Area, And Volume 11 Data Analysis And Probability 12 Angle Relationships And Transformations CSR Contents Of Student Resources ChapterCSR: Contents Of Student Resources
Chapter Questions Section: Chapter Questions
Problem 1.1P Problem 1.2P Problem 1.3P Problem 1.4P Problem 1.5P Problem 1.6P Problem 1.7P Problem 1.8P Problem 1.9P Problem 1.10P Problem 1.11P Problem 1.12P Problem 1.13P Problem 1.14P Problem 1.15P Problem 1.16P Problem 2.1P Problem 2.2P Problem 2.3P Problem 2.4P Problem 2.5P Problem 2.6P Problem 2.7P Problem 2.8P Problem 2.9P Problem 2.10P Problem 2.11P Problem 2.12P Problem 2.13P Problem 2.14P Problem 3.1P Problem 3.2P Problem 3.3P Problem 3.4P Problem 3.5P Problem 3.6P Problem 3.7P Problem 3.8P Problem 3.9P Problem 3.10P Problem 3.11P Problem 3.12P Problem 3.13P Problem 3.14P Problem 3.15P Problem 3.16P Problem 4.1P Problem 4.2P Problem 4.3P Problem 4.4P Problem 4.5P Problem 4.6P Problem 4.7P Problem 4.8P Problem 4.9P Problem 4.10P Problem 4.11P Problem 4.12P Problem 5.1P Problem 5.2P Problem 5.3P Problem 5.4P Problem 5.5P Problem 5.6P Problem 5.7P Problem 5.8P Problem 5.9P Problem 5.10P Problem 5.11P Problem 5.12P Problem 5.13P Problem 5.14P Problem 5.15P Problem 5.16P Problem 6.1P Problem 6.2P Problem 6.3P Problem 6.4P Problem 6.5P Problem 6.6P Problem 6.7P Problem 6.8P Problem 6.9P Problem 6.10P Problem 6.11P Problem 6.12P Problem 6.13P Problem 6.14P Problem 6.15P Problem 6.16P Problem 7.1P Problem 7.2P Problem 7.3P Problem 7.4P Problem 7.5P Problem 7.6P Problem 7.7P Problem 7.8P Problem 7.9P Problem 7.10P Problem 7.11P Problem 7.12P Problem 7.13P Problem 7.14P Problem 7.15P Problem 7.16P Problem 7.17P Problem 7.18P Problem 7.19P Problem 7.20P Problem 8.1P Problem 8.2P Problem 8.3P Problem 8.4P Problem 8.5P Problem 8.6P Problem 8.7P Problem 8.8P Problem 8.9P Problem 8.10P Problem 8.11P Problem 8.12P Problem 9.1P Problem 9.2P Problem 9.3P Problem 9.4P Problem 9.5P Problem 9.6P Problem 9.7P Problem 9.8P Problem 9.9P Problem 9.10P Problem 9.11P Problem 9.12P Problem 9.13P Problem 9.14P Problem 9.15P Problem 9.16P Problem 9.17P Problem 9.18P Problem 9.19P Problem 9.20P Problem 9.21P Problem 9.22P Problem 9.23P Problem 9.24P Problem 9.25P Problem 10.1P Problem 10.2P Problem 10.3P Problem 10.4P Problem 10.5P Problem 10.6P Problem 10.7P Problem 10.8P Problem 10.9P Problem 10.10P Problem 10.11P Problem 10.12P Problem 10.13P Problem 10.14P Problem 10.15P Problem 10.16P Problem 10.17P Problem 10.18P Problem 10.19P Problem 10.20P Problem 11.1P Problem 11.2P Problem 11.3P Problem 11.4P Problem 11.5P Problem 11.6P Problem 11.7P Problem 11.8P Problem 11.9P Problem 11.10P Problem 11.11P Problem 11.12P Problem 11.13P Problem 11.14P Problem 11.15P Problem 11.16P Problem 12.1P Problem 12.2P Problem 12.3P Problem 12.4P Problem 12.5P Problem 12.6P Problem 12.7P Problem 13.1P Problem 13.2P Problem 13.3P Problem 13.4P Problem 13.5P Problem 13.6P Problem 13.7P Problem 14.1P Problem 14.2P Problem 14.3P Problem 14.4P Problem 14.5P Problem 14.6P Problem 14.7P Problem 15.1P Problem 15.2P Problem 15.3P Problem 15.4P Problem 16.1P Problem 16.2P Problem 16.3P Problem 16.4P Problem 16.5P Problem 16.6P Problem 16.7P Problem 16.8P Problem 17.1P Problem 17.2P Problem 17.3P Problem 17.4P Problem 17.5P Problem 17.6P Problem 18.1P Problem 18.2P Problem 18.3P Problem 18.4P Problem 18.5P Problem 18.6P Problem 18.7P Problem 18.8P Problem 18.9P Problem 18.10P Problem 18.11P Problem 18.12P Problem 18.13P Problem 18.14P Problem 18.15P Problem 18.16P Problem 19.1P Problem 19.2P Problem 19.3P Problem 19.4P Problem 19.5P Problem 19.6P Problem 19.7P Problem 19.8P Problem 19.9P Problem 19.10P Problem 19.11P Problem 19.12P Problem 19.13P Problem 19.14P Problem 19.15P Problem 19.16P Problem 20.1P Problem 20.2P Problem 20.3P Problem 20.4P Problem 20.5P Problem 20.6P Problem 20.7P Problem 20.8P Problem 21.1P Problem 21.2P Problem 21.3P Problem 21.4P Problem 21.5P Problem 21.6P Problem 21.7P Problem 21.8P Problem 21.9P Problem 22.1P Problem 22.2P Problem 22.3P Problem 22.4P Problem 22.5P Problem 22.6P Problem 22.7P Problem 22.8P Problem 22.9P Problem 23.1P Problem 23.2P Problem 23.3P Problem 23.4P Problem 23.5P Problem 23.6P Problem 23.7P Problem 23.8P Problem 23.9P Problem 24.1P Problem 24.2P Problem 24.3P Problem 24.4P Problem 24.5P Problem 24.6P Problem 24.7P Problem 24.8P Problem 25.1P Problem 25.2P Problem 25.3P Problem 25.4P Problem 25.5P Problem 25.6P Problem 25.7P Problem 26.1P Problem 26.2P Problem 26.3P Problem 26.4P Problem 26.5P Problem 27.1P Problem 27.2P Problem 27.3P Problem 28.1P Problem 28.2P Problem 28.3P Problem 29.1P Problem 29.2P Problem 29.3P Problem 29.4P Problem 29.5P Problem 29.6P Problem 30.1P Problem 30.2P Problem 30.3P Problem 31.1P Problem 31.2P Problem 31.3P Problem 32.1P Problem 32.2P Problem 32.3P Problem 33.1P Problem 33.2P Problem 33.3P Problem 34.1P Problem 34.2P Problem 34.3P Problem 1.1EP Problem 1.2EP Problem 1.3EP Problem 1.4EP Problem 1.5EP Problem 1.6EP Problem 1.7EP Problem 1.8EP Problem 1.9EP Problem 1.10EP Problem 1.11EP Problem 1.12EP Problem 1.13EP Problem 1.14EP Problem 1.15EP Problem 1.16EP Problem 1.17EP Problem 1.18EP Problem 1.19EP Problem 1.20EP Problem 1.21EP Problem 1.22EP Problem 1.23EP Problem 1.24EP Problem 1.25EP Problem 1.26EP Problem 1.27EP Problem 1.28EP Problem 1.29EP Problem 1.30EP Problem 1.31EP Problem 1.32EP Problem 1.33EP Problem 1.34EP Problem 1.35EP Problem 1.36EP Problem 1.37EP Problem 1.38EP Problem 1.39EP Problem 1.40EP Problem 1.41EP Problem 2.1EP Problem 2.2EP Problem 2.3EP Problem 2.4EP Problem 2.5EP Problem 2.6EP Problem 2.7EP Problem 2.8EP Problem 2.9EP Problem 2.10EP Problem 2.11EP Problem 2.12EP Problem 2.13EP Problem 2.14EP Problem 2.15EP Problem 2.16EP Problem 2.17EP Problem 2.18EP Problem 2.19EP Problem 2.20EP Problem 2.21EP Problem 2.22EP Problem 2.23EP Problem 2.24EP Problem 2.25EP Problem 2.26EP Problem 2.27EP Problem 2.28EP Problem 2.29EP Problem 2.30EP Problem 2.31EP Problem 2.32EP Problem 2.33EP Problem 2.34EP Problem 2.35EP Problem 2.36EP Problem 2.37EP Problem 2.38EP Problem 2.39EP Problem 2.40EP Problem 2.41EP Problem 2.42EP Problem 2.43EP Problem 2.44EP Problem 2.45EP Problem 2.46EP Problem 2.47EP Problem 2.48EP Problem 2.49EP Problem 2.50EP Problem 2.51EP Problem 2.52EP Problem 2.53EP Problem 2.54EP Problem 2.55EP Problem 2.56EP Problem 2.57EP Problem 2.58EP Problem 2.59EP Problem 3.1EP Problem 3.2EP Problem 3.3EP Problem 3.4EP Problem 3.5EP Problem 3.6EP Problem 3.7EP Problem 3.8EP Problem 3.9EP Problem 3.10EP Problem 3.11EP Problem 3.12EP Problem 3.13EP Problem 3.14EP Problem 3.15EP Problem 3.16EP Problem 3.17EP Problem 3.18EP Problem 3.19EP Problem 3.20EP Problem 3.21EP Problem 3.22EP Problem 3.23EP Problem 3.24EP Problem 3.25EP Problem 3.26EP Problem 3.27EP Problem 3.28EP Problem 3.29EP Problem 3.30EP Problem 3.31EP Problem 3.32EP Problem 3.33EP Problem 3.34EP Problem 3.35EP Problem 3.36EP Problem 3.37EP Problem 3.38EP Problem 3.39EP Problem 3.40EP Problem 3.41EP Problem 3.42EP Problem 3.43EP Problem 3.44EP Problem 3.45EP Problem 3.46EP Problem 3.47EP Problem 3.48EP Problem 3.49EP Problem 3.50EP Problem 3.51EP Problem 3.52EP Problem 3.53EP Problem 3.54EP Problem 3.55EP Problem 3.56EP Problem 3.57EP Problem 3.58EP Problem 3.59EP Problem 3.60EP Problem 4.1EP Problem 4.2EP Problem 4.3EP Problem 4.4EP Problem 4.5EP Problem 4.6EP Problem 4.7EP Problem 4.8EP Problem 4.9EP Problem 4.10EP Problem 4.11EP Problem 4.12EP Problem 4.13EP Problem 4.14EP Problem 4.15EP Problem 4.16EP Problem 4.17EP Problem 4.18EP Problem 4.19EP Problem 4.20EP Problem 4.21EP Problem 4.22EP Problem 4.23EP Problem 4.24EP Problem 4.25EP Problem 4.26EP Problem 4.27EP Problem 4.28EP Problem 4.29EP Problem 4.30EP Problem 4.31EP Problem 4.32EP Problem 4.33EP Problem 4.34EP Problem 4.35EP Problem 4.36EP Problem 4.37EP Problem 4.38EP Problem 4.39EP Problem 4.40EP Problem 4.41EP Problem 4.42EP Problem 4.43EP Problem 4.44EP Problem 4.45EP Problem 4.46EP Problem 4.47EP Problem 4.48EP Problem 4.49EP Problem 4.50EP Problem 4.51EP Problem 4.52EP Problem 5.1EP Problem 5.2EP Problem 5.3EP Problem 5.4EP Problem 5.5EP Problem 5.6EP Problem 5.7EP Problem 5.8EP Problem 5.9EP Problem 5.10EP Problem 5.11EP Problem 5.12EP Problem 5.13EP Problem 5.14EP Problem 5.15EP Problem 5.16EP Problem 5.17EP Problem 5.18EP Problem 5.19EP Problem 5.20EP Problem 5.21EP Problem 5.22EP Problem 5.23EP Problem 5.24EP Problem 5.25EP Problem 5.26EP Problem 5.27EP Problem 5.28EP Problem 5.29EP Problem 5.30EP Problem 5.31EP Problem 5.32EP Problem 5.33EP Problem 5.34EP Problem 5.35EP Problem 5.36EP Problem 5.37EP Problem 5.38EP Problem 5.39EP Problem 5.40EP Problem 5.41EP Problem 5.42EP Problem 5.43EP Problem 5.44EP Problem 6.1EP Problem 6.2EP Problem 6.3EP Problem 6.4EP Problem 6.5EP Problem 6.6EP Problem 6.7EP Problem 6.8EP Problem 6.9EP Problem 6.10EP Problem 6.11EP Problem 6.12EP Problem 6.13EP Problem 6.14EP Problem 6.15EP Problem 6.16EP Problem 6.17EP Problem 6.18EP Problem 6.19EP Problem 6.20EP Problem 6.21EP Problem 6.22EP Problem 6.23EP Problem 6.24EP Problem 6.25EP Problem 6.26EP Problem 6.27EP Problem 6.28EP Problem 6.29EP Problem 6.30EP Problem 6.31EP Problem 6.32EP Problem 6.33EP Problem 7.1EP Problem 7.2EP Problem 7.3EP Problem 7.4EP Problem 7.5EP Problem 7.6EP Problem 7.7EP Problem 7.8EP Problem 7.9EP Problem 7.10EP Problem 7.11EP Problem 7.12EP Problem 7.13EP Problem 7.14EP Problem 7.15EP Problem 7.16EP Problem 7.17EP Problem 7.18EP Problem 7.19EP Problem 7.20EP Problem 7.21EP Problem 7.22EP Problem 7.23EP Problem 7.24EP Problem 7.25EP Problem 7.26EP Problem 7.27EP Problem 7.28EP Problem 7.29EP Problem 7.30EP Problem 7.31EP Problem 7.32EP Problem 7.33EP Problem 7.34EP Problem 7.35EP Problem 7.36EP Problem 8.1EP Problem 8.2EP Problem 8.3EP Problem 8.4EP Problem 8.5EP Problem 8.6EP Problem 8.7EP Problem 8.8EP Problem 8.9EP Problem 8.10EP Problem 8.11EP Problem 8.12EP Problem 8.13EP Problem 8.14EP Problem 8.15EP Problem 8.16EP Problem 8.17EP Problem 8.18EP Problem 8.19EP Problem 8.20EP Problem 8.21EP Problem 8.22EP Problem 8.23EP Problem 8.24EP Problem 8.25EP Problem 8.26EP Problem 8.27EP Problem 8.28EP Problem 8.29EP Problem 8.30EP Problem 8.31EP Problem 8.32EP Problem 8.33EP Problem 8.34EP Problem 8.35EP Problem 8.36EP Problem 8.37EP Problem 8.38EP Problem 8.39EP Problem 8.40EP Problem 8.41EP Problem 8.42EP Problem 9.1EP Problem 9.2EP Problem 9.3EP Problem 9.4EP Problem 9.5EP Problem 9.6EP Problem 9.7EP Problem 9.8EP Problem 9.9EP Problem 9.10EP Problem 9.11EP Problem 9.12EP Problem 9.13EP Problem 9.14EP Problem 9.15EP Problem 9.16EP Problem 9.17EP Problem 9.18EP Problem 9.19EP Problem 9.20EP Problem 9.21EP Problem 9.22EP Problem 9.23EP Problem 9.24EP Problem 9.25EP Problem 9.26EP Problem 9.27EP Problem 9.28EP Problem 9.29EP Problem 9.30EP Problem 9.31EP Problem 9.32EP Problem 9.33EP Problem 9.34EP Problem 9.35EP Problem 9.36EP Problem 10.1EP Problem 10.2EP Problem 10.3EP Problem 10.4EP Problem 10.5EP Problem 10.6EP Problem 10.7EP Problem 10.8EP Problem 10.9EP Problem 10.10EP Problem 10.11EP Problem 10.12EP Problem 10.13EP Problem 10.14EP Problem 10.15EP Problem 10.16EP Problem 10.17EP Problem 10.18EP Problem 10.19EP Problem 10.20EP Problem 10.21EP Problem 10.22EP Problem 10.23EP Problem 10.24EP Problem 10.25EP Problem 10.26EP Problem 10.27EP Problem 10.28EP Problem 11.1EP Problem 11.2EP Problem 11.3EP Problem 11.4EP Problem 11.5EP Problem 11.6EP Problem 11.7EP Problem 11.8EP Problem 11.9EP Problem 11.10EP Problem 11.11EP Problem 11.12EP Problem 11.13EP Problem 11.14EP Problem 11.15EP Problem 11.16EP Problem 11.17EP Problem 11.18EP Problem 11.19EP Problem 11.20EP Problem 11.21EP Problem 11.22EP Problem 12.1EP Problem 12.2EP Problem 12.3EP Problem 12.4EP Problem 12.5EP Problem 12.6EP Problem 12.7EP Problem 12.8EP Problem 12.9EP Problem 12.10EP Problem 12.11EP Problem 12.12EP Problem 12.13EP Problem 12.14EP Problem 12.15EP Problem 12.16EP Problem 12.17EP Problem 12.18EP Problem 12.19EP Problem 12.20EP Problem 12.21EP Problem 1.39EP
Related questions
With this given triangle , how would I get the value of x? With the triangle having two degrees?
Transcribed Image Text: **Finding the Length of a Side in a Right Triangle**
**Problem Statement:**
**Find \( x \) correct to 2 decimal places.**
**NOTE: The triangle is NOT drawn to scale.**
**Diagram Description:**
- The given diagram represents a right triangle outlined in blue.
- The right angle is located at the bottom left corner of the triangle.
- One of the legs of the triangle adjacent to the right angle is labeled as 82 units.
- The angle opposite this leg is labeled as 57 degrees.
- The other non-right angle, adjacent to the unknown side \( x \), is labeled as 32 degrees.
- The base of the triangle, opposite the right angle, is designated as \( x \).
**To Solve:**
1. Use appropriate trigonometric ratios such as sine, cosine or tangent to find \( x \).
2. Considering the given angles, the cosine of 57 degrees can be used since it relates the adjacent side (82 units) to the hypotenuse (x).
\[ \cos(57^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{82}{x} \]
3. Solve for \( x \):
\[ x = \frac{82}{\cos(57^\circ)} \]
4. Calculate and round the result to 2 decimal places.
**Answer Box:**
\( x \approx \) [Input field]
**Question Help:**
- Worked Example 1
- Message instructor
Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).
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![**Finding the Length of a Side in a Right Triangle**
**Problem Statement:**
**Find \( x \) correct to 2 decimal places.**
**NOTE: The triangle is NOT drawn to scale.**
**Diagram Description:**
- The given diagram represents a right triangle outlined in blue.
- The right angle is located at the bottom left corner of the triangle.
- One of the legs of the triangle adjacent to the right angle is labeled as 82 units.
- The angle opposite this leg is labeled as 57 degrees.
- The other non-right angle, adjacent to the unknown side \( x \), is labeled as 32 degrees.
- The base of the triangle, opposite the right angle, is designated as \( x \).
**To Solve:**
1. Use appropriate trigonometric ratios such as sine, cosine or tangent to find \( x \).
2. Considering the given angles, the cosine of 57 degrees can be used since it relates the adjacent side (82 units) to the hypotenuse (x).
\[ \cos(57^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{82}{x} \]
3. Solve for \( x \):
\[ x = \frac{82}{\cos(57^\circ)} \]
4. Calculate and round the result to 2 decimal places.
**Answer Box:**
\( x \approx \) [Input field]
**Question Help:**
- Worked Example 1
- Message instructor](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F346b36e0-a4d8-47d7-8bd1-1ad776cb1cf3%2F11ad608f-2167-4124-99b9-57e446aa6816%2Falxhjt_processed.png&w=3840&q=75)
