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A Survey line BAC crosses a river. A and C being on the near and distant banks Respectively. Standing at D , A Point 50 meters measured perpendicularly to AB from A. The bearing of C and B are 320degree and 230degree at D Respectively . AB being 25meters. Find the width of the river?
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A Survey line BAC crosses a river. A and C being on the near and dista...
Solution:
Given:
AB = 25 meters
AD = 50 meters
∠ADB = 90 degrees
∠BDC = 320 degrees
∠ADB = 230 degrees
To find:
Width of the river (BC)
Approach:
We can use trigonometry to solve this problem. We will first find the length of BD using the sine rule and then use the cosine rule to find the length of BC.
Calculation:
Let's first find the length of BD using the sine rule.
sin(∠ADB)/AB = sin(∠BDA)/BD
sin(90)/25 = sin(230)/BD
BD = 25*sin(230)/sin(90) = -24.17 meters (negative sign indicates that B is on the opposite side of A)
Now, let's find the length of BC using the cosine rule.
BC^2 = BD^2 + CD^2 - 2*BD*CD*cos(∠BDC)
BC^2 = (-24.17)^2 + CD^2 - 2*(-24.17)*CD*cos(320)
BC^2 = 582.91 + CD^2 + 48.34*CD
Similarly, BC^2 = 625 + CD^2 - 25*CD*cos(230)
Equating both the equations, we get:
582.91 + CD^2 + 48.34*CD = 625 + CD^2 - 25*CD*cos(230)
25*CD*cos(230) + 48.34*CD = 42.09
CD = 0.648 meters
Therefore, BC = CD/cos(320) = 0.75 meters
Answer:
The width of the river (BC) is 0.75 meters.
Explanation:
The given survey line BAC crosses a river. We are given the coordinates of A and C and the length of AB. We are also given the bearing of B and C from point D, where D is a point on the line perpendicular to AB and 50 meters away from A. We are asked to find the width of the river.
We can solve this problem using trigonometry. First, we find the length of BD using the sine rule. Then, we use the cosine rule to find the length of BC. We equate two equations obtained from the cosine rule to find the value of CD, which is the distance between D and C. Finally, we use the value of CD and the bearing of C from D to find the width of the river (BC).
Given:
AB = 25 meters
AD = 50 meters
∠ADB = 90 degrees
∠BDC = 320 degrees
∠ADB = 230 degrees
To find:
Width of the river (BC)
Approach:
We can use trigonometry to solve this problem. We will first find the length of BD using the sine rule and then use the cosine rule to find the length of BC.
Calculation:
Let's first find the length of BD using the sine rule.
sin(∠ADB)/AB = sin(∠BDA)/BD
sin(90)/25 = sin(230)/BD
BD = 25*sin(230)/sin(90) = -24.17 meters (negative sign indicates that B is on the opposite side of A)
Now, let's find the length of BC using the cosine rule.
BC^2 = BD^2 + CD^2 - 2*BD*CD*cos(∠BDC)
BC^2 = (-24.17)^2 + CD^2 - 2*(-24.17)*CD*cos(320)
BC^2 = 582.91 + CD^2 + 48.34*CD
Similarly, BC^2 = 625 + CD^2 - 25*CD*cos(230)
Equating both the equations, we get:
582.91 + CD^2 + 48.34*CD = 625 + CD^2 - 25*CD*cos(230)
25*CD*cos(230) + 48.34*CD = 42.09
CD = 0.648 meters
Therefore, BC = CD/cos(320) = 0.75 meters
Answer:
The width of the river (BC) is 0.75 meters.
Explanation:
The given survey line BAC crosses a river. We are given the coordinates of A and C and the length of AB. We are also given the bearing of B and C from point D, where D is a point on the line perpendicular to AB and 50 meters away from A. We are asked to find the width of the river.
We can solve this problem using trigonometry. First, we find the length of BD using the sine rule. Then, we use the cosine rule to find the length of BC. We equate two equations obtained from the cosine rule to find the value of CD, which is the distance between D and C. Finally, we use the value of CD and the bearing of C from D to find the width of the river (BC).
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A Survey line BAC crosses a river. A and C being on the near and distant banks Respectively. Standing at D , A Point 50 meters measured perpendicularly to AB from A. The bearing of C and B are 320degree and 230degree at D Respectively . AB being 25meters. Find the width of the river?
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A Survey line BAC crosses a river. A and C being on the near and distant banks Respectively. Standing at D , A Point 50 meters measured perpendicularly to AB from A. The bearing of C and B are 320degree and 230degree at D Respectively . AB being 25meters. Find the width of the river? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A Survey line BAC crosses a river. A and C being on the near and distant banks Respectively. Standing at D , A Point 50 meters measured perpendicularly to AB from A. The bearing of C and B are 320degree and 230degree at D Respectively . AB being 25meters. Find the width of the river? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Survey line BAC crosses a river. A and C being on the near and distant banks Respectively. Standing at D , A Point 50 meters measured perpendicularly to AB from A. The bearing of C and B are 320degree and 230degree at D Respectively . AB being 25meters. Find the width of the river?.
A Survey line BAC crosses a river. A and C being on the near and distant banks Respectively. Standing at D , A Point 50 meters measured perpendicularly to AB from A. The bearing of C and B are 320degree and 230degree at D Respectively . AB being 25meters. Find the width of the river? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A Survey line BAC crosses a river. A and C being on the near and distant banks Respectively. Standing at D , A Point 50 meters measured perpendicularly to AB from A. The bearing of C and B are 320degree and 230degree at D Respectively . AB being 25meters. Find the width of the river? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Survey line BAC crosses a river. A and C being on the near and distant banks Respectively. Standing at D , A Point 50 meters measured perpendicularly to AB from A. The bearing of C and B are 320degree and 230degree at D Respectively . AB being 25meters. Find the width of the river?.
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A Survey line BAC crosses a river. A and C being on the near and distant banks Respectively. Standing at D , A Point 50 meters measured perpendicularly to AB from A. The bearing of C and B are 320degree and 230degree at D Respectively . AB being 25meters. Find the width of the river?, a detailed solution for A Survey line BAC crosses a river. A and C being on the near and distant banks Respectively. Standing at D , A Point 50 meters measured perpendicularly to AB from A. The bearing of C and B are 320degree and 230degree at D Respectively . AB being 25meters. Find the width of the river? has been provided alongside types of A Survey line BAC crosses a river. A and C being on the near and distant banks Respectively. Standing at D , A Point 50 meters measured perpendicularly to AB from A. The bearing of C and B are 320degree and 230degree at D Respectively . AB being 25meters. Find the width of the river? theory, EduRev gives you an
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