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
Problem 1RQ
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![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a1a7db6-8f8f-43d1-b008-03a5d653c710%2F6147a993-6ecf-4d2c-bb57-a2350e311c2a%2F4yr0uur_processed.png&w=3840&q=75)
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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