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1. use pith. theorem to find the lengt b. b= sqrt(x1-x2)^2 +(y1-y2)^2 2. use the laws of sines to find angles  A and C 3. find all angles of all triangles inside

1. use pith. theorem to find the lengt b. b= sqrt(x1-x2)^2 +(y1-y2)^2 2. use the laws of sines to find angles  A and C 3. find all angles of all triangles inside

Advanced Engineering Mathematics
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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Question

Find the coordinates at the angle B. from the given information:

1. distance c=88.565 (ft)

    distance a = 172.302 (ft)

 

2.   Coordinates of BM-1:  x1= 1176382.267 (ft); y1=1882965.144 (ft)

      Coordinates of BM-2:  x2=1176249.348 (ft); y2=1883141.718 (ft)

 

3. angle B = 108

 

 

Steps to follow :

1. use pith. theorem to find the lengt b. b= sqrt(x1-x2)^2 +(y1-y2)^2

2. use the laws of sines to find angles  A and C

3. find all angles of all triangles inside 

4. now find x and y coordinates at the point at the angle B using those angles.

f.example:  sin = (y-y2)/a  and cos=(x2-x)/a  

**Diagram Explanation:** The image shows a geometric diagram featuring a triangle formed by three points labeled as A, B, and X. There are two base stations (BM-1 and BM-2) represented by their coordinates (x₁, y₁) and (x₂, y₂), respectively. The triangle is formed by points A, B, and BM-2, with sides labeled as a, b, and c. The angles are also marked, with one labeled as ∠B. **Given Data:** - **Distance c** = 88.565 feet - **Distance a** = 172.302 feet **Coordinates:** - **BM-1**: - x₁ = 1176382.267 feet - y₁ = 1882965.144 feet - **BM-2**: - x₂ = 1176249.348 feet - y₂ = 1883741.718 feet **Angular Measure:** - **∠B** = 108° (degrees)
Transcribed Image Text:**Diagram Explanation:** The image shows a geometric diagram featuring a triangle formed by three points labeled as A, B, and X. There are two base stations (BM-1 and BM-2) represented by their coordinates (x₁, y₁) and (x₂, y₂), respectively. The triangle is formed by points A, B, and BM-2, with sides labeled as a, b, and c. The angles are also marked, with one labeled as ∠B. **Given Data:** - **Distance c** = 88.565 feet - **Distance a** = 172.302 feet **Coordinates:** - **BM-1**: - x₁ = 1176382.267 feet - y₁ = 1882965.144 feet - **BM-2**: - x₂ = 1176249.348 feet - y₂ = 1883741.718 feet **Angular Measure:** - **∠B** = 108° (degrees)
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