Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Question 2: Solve the Triangle Below
You are given a right triangle \( \triangle ABC \).
- **Angle A**: 60 degrees
- **Side \( AB \)**: 10 units
- **Angle C**: 90 degrees (right angle)
**Labels on Diagram:**
- **Side \( BC \)**: labeled as \( a \) (opposite angle A)
- **Side \( AC \)**: labeled as \( b \) (adjacent to angle A)
Your task is to find the lengths of sides \( a \) and \( b \).
### Explanation:
The triangle is a right triangle with one angle measuring 60 degrees and the hypotenuse measuring 10 units. Use trigonometric ratios (sine, cosine) to find the lengths of the unknown sides.
1. **To find \( a \):**
\[
\sin(60^\circ) = \frac{a}{10}
\]
2. **To find \( b \):**
\[
\cos(60^\circ) = \frac{b}{10}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8814a965-aa31-4a1a-853b-04fa9e01dcc1%2F1b7330ad-13bf-4084-8d5d-53a7ec210c52%2Fli009db_processed.png&w=3840&q=75)
Transcribed Image Text:### Question 2: Solve the Triangle Below
You are given a right triangle \( \triangle ABC \).
- **Angle A**: 60 degrees
- **Side \( AB \)**: 10 units
- **Angle C**: 90 degrees (right angle)
**Labels on Diagram:**
- **Side \( BC \)**: labeled as \( a \) (opposite angle A)
- **Side \( AC \)**: labeled as \( b \) (adjacent to angle A)
Your task is to find the lengths of sides \( a \) and \( b \).
### Explanation:
The triangle is a right triangle with one angle measuring 60 degrees and the hypotenuse measuring 10 units. Use trigonometric ratios (sine, cosine) to find the lengths of the unknown sides.
1. **To find \( a \):**
\[
\sin(60^\circ) = \frac{a}{10}
\]
2. **To find \( b \):**
\[
\cos(60^\circ) = \frac{b}{10}
\]
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