Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such than ZCAB = 51.2°. Find the distance across the lake from A to B. B 511 yd NOTE: The triangle is NOT drawn to scale. distance = yd 325 yd 51.2° 9 Enter your answer as a number: your answer should be accurate to 2 decimal places.
Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such than ZCAB = 51.2°. Find the distance across the lake from A to B. B 511 yd NOTE: The triangle is NOT drawn to scale. distance = yd 325 yd 51.2° 9 Enter your answer as a number: your answer should be accurate to 2 decimal places.
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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![### Problem Description
Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such that \(\angle CAB = 51.2^\circ\). Find the distance across the lake from A to B.
### Illustration
The diagram shows a triangle with vertices labeled A, B, and C.
- Line segment \(CA\) measures 325 yards.
- Line segment \(CB\) measures 511 yards.
- \(\angle CAB\) is marked as 51.2 degrees.
The path across the lake forms the missing side of the triangle from point A to B.
### Note
- The triangle is NOT drawn to scale.
### Calculation
To find the distance across the lake from A to B, enter your answer as a number, and ensure it is accurate to two decimal places.
\[ \text{distance} = \_\_\_\_ \text{ yd} \]
### Instructions
- Apply the law of cosines to calculate the distance \(AB\):
\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]
- Where:
- \(a = 325\) yd (CA)
- \(b = 511\) yd (CB)
- \(C = 51.2^\circ\) (angle CAB)
\[ \text{distance} = \text{calculated value} \] (rounded to two decimal places)
Enter your answer in the provided space.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b1e272d-5cc1-4d39-8036-66e03e6cc3b4%2Fcf3c3a4c-022b-4d55-b813-00d45356755b%2Fl0orwsp_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description
Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such that \(\angle CAB = 51.2^\circ\). Find the distance across the lake from A to B.
### Illustration
The diagram shows a triangle with vertices labeled A, B, and C.
- Line segment \(CA\) measures 325 yards.
- Line segment \(CB\) measures 511 yards.
- \(\angle CAB\) is marked as 51.2 degrees.
The path across the lake forms the missing side of the triangle from point A to B.
### Note
- The triangle is NOT drawn to scale.
### Calculation
To find the distance across the lake from A to B, enter your answer as a number, and ensure it is accurate to two decimal places.
\[ \text{distance} = \_\_\_\_ \text{ yd} \]
### Instructions
- Apply the law of cosines to calculate the distance \(AB\):
\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]
- Where:
- \(a = 325\) yd (CA)
- \(b = 511\) yd (CB)
- \(C = 51.2^\circ\) (angle CAB)
\[ \text{distance} = \text{calculated value} \] (rounded to two decimal places)
Enter your answer in the provided space.
Expert Solution
Step 1
For any triangle: , using the cosine rule, it can be written that: .
The roots of the quadratic equation: is calculated using the quadratic formula: .
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