a = 30° 8 a C = 45° 60° 2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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please and thank you!

**Problem Description:**

For the right triangles below, find the exact values of the side lengths \( a \) and \( c \). If necessary, write your responses in simplified radical form.

**Diagrams:**

1. **First Triangle:**
   - Right triangle with angles \( 45^\circ \), \( 45^\circ \), and \( 90^\circ \).
   - Hypotenuse is labeled as 2.
   - One leg is \( a \).

2. **Second Triangle:**
   - Right triangle with angles \( 30^\circ \), \( 60^\circ \), and \( 90^\circ \).
   - Opposite the \( 30^\circ \) angle is a side labeled 8.
   - Hypotenuse is marked as \( c \).

**Solution Requirements:**
- Find \( a \) for the first triangle.
- Find \( c \) for the second triangle.
- Provide answers in simplified radical form if necessary.

**Input Boxes:**

- \( a = \) [Input Box]
- \( c = \) [Input Box]

**Options:**
- Simplified radical form notation and basic mathematical symbols are available to assist in forming responses.
Transcribed Image Text:**Problem Description:** For the right triangles below, find the exact values of the side lengths \( a \) and \( c \). If necessary, write your responses in simplified radical form. **Diagrams:** 1. **First Triangle:** - Right triangle with angles \( 45^\circ \), \( 45^\circ \), and \( 90^\circ \). - Hypotenuse is labeled as 2. - One leg is \( a \). 2. **Second Triangle:** - Right triangle with angles \( 30^\circ \), \( 60^\circ \), and \( 90^\circ \). - Opposite the \( 30^\circ \) angle is a side labeled 8. - Hypotenuse is marked as \( c \). **Solution Requirements:** - Find \( a \) for the first triangle. - Find \( c \) for the second triangle. - Provide answers in simplified radical form if necessary. **Input Boxes:** - \( a = \) [Input Box] - \( c = \) [Input Box] **Options:** - Simplified radical form notation and basic mathematical symbols are available to assist in forming responses.
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