Solve for the missing measures in the diagram (side lengths and angles). Round the angle measures to the nearest tenth. The side length should be an integer. G m/G= mZH = GH = 12 5 H
Solve for the missing measures in the diagram (side lengths and angles). Round the angle measures to the nearest tenth. The side length should be an integer. G m/G= mZH = GH = 12 5 H
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
![**Solve for the missing measures in the diagram (side lengths and angles). Round the angle measures to the nearest tenth. The side length should be an integer.**
![Right Triangle Diagram]
- **Angle \( \angle G \) Measure (m\( \angle G \))**:
- **Angle \( \angle H \) Measure (m\( \angle H \))**:
- **Side Length \( GH \)**:
**Diagram Details:**
The diagram depicts a right triangle with the following information:
- Hypotenuse \( GH = 12 \)
- One leg \( IH = 5 \)
- The right angle \( \angle I \)
To find the missing measures:
1. **Finding Side \( GH \):**
Use the Pythagorean theorem \( a^2 + b^2 = c^2 \):
\[
GI = \sqrt{12^2 - 5^2} = \sqrt{144 - 25} = \sqrt{119} \approx 10.9
\]
2. **Finding the angles \( \angle G \) and \( \angle H \):**
- \( \angle G = \arcsin\left(\frac{5}{12}\right) \approx 24.6^{\circ} \)
- \( \angle H = 90^{\circ} - \arcsin\left(\frac{5}{12}\right) \approx 65.4^{\circ} \)
**Final Measures:**
- \( m\angle G = 24.6^{\circ} \)
- \( m\angle H = 65.4^{\circ} \)
- \( GH \approx 10.9 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6db432ab-37f5-462a-9e25-be8c030c3775%2F105e1efc-797e-4349-86da-36fe675b0c6b%2Feyxv6ga_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve for the missing measures in the diagram (side lengths and angles). Round the angle measures to the nearest tenth. The side length should be an integer.**
![Right Triangle Diagram]
- **Angle \( \angle G \) Measure (m\( \angle G \))**:
- **Angle \( \angle H \) Measure (m\( \angle H \))**:
- **Side Length \( GH \)**:
**Diagram Details:**
The diagram depicts a right triangle with the following information:
- Hypotenuse \( GH = 12 \)
- One leg \( IH = 5 \)
- The right angle \( \angle I \)
To find the missing measures:
1. **Finding Side \( GH \):**
Use the Pythagorean theorem \( a^2 + b^2 = c^2 \):
\[
GI = \sqrt{12^2 - 5^2} = \sqrt{144 - 25} = \sqrt{119} \approx 10.9
\]
2. **Finding the angles \( \angle G \) and \( \angle H \):**
- \( \angle G = \arcsin\left(\frac{5}{12}\right) \approx 24.6^{\circ} \)
- \( \angle H = 90^{\circ} - \arcsin\left(\frac{5}{12}\right) \approx 65.4^{\circ} \)
**Final Measures:**
- \( m\angle G = 24.6^{\circ} \)
- \( m\angle H = 65.4^{\circ} \)
- \( GH \approx 10.9 \)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning