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Asurvey line BAC crosses a river as shown in the figure, A and C voids on the near and distant banks, respectively.
Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,
respectively. The angle BDA equal to theta=60�. What is the width of the river AC?
ANS 50/1.732 m?
Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,
respectively. The angle BDA equal to theta=60�. What is the width of the river AC?
ANS 50/1.732 m?
Most Upvoted Answer
Asurvey line BAC crosses a river as shown in the figure, A and C voids...
**Solution:**
To find the width of the river AC, we can use the concept of trigonometry and the given information about the bearings and angles.
**1. Draw the given information:**
- Draw a line AB to represent the survey line BAC.
- Mark points A and C on the near and distant banks, respectively.
- Draw a perpendicular line BD from point D to line AB.
- Measure the distance BD as 50 m.
- Label the bearings of C and B as 320° and 230°, respectively.
- Label the angle BDA as θ = 60°.
**2. Determine the angles:**
- Since the bearing of C is 320°, we can determine the angle ACD as 360° - 320° = 40°.
- Similarly, the angle ABD can be determined as 360° - 230° = 130°.
**3. Use trigonometry to find the width of the river:**
- We can use the sine rule to find the width of the river AC.
- The sine rule states that for any triangle ABC, the following ratio holds true: (sin A) / a = (sin B) / b = (sin C) / c.
- In our case, we can use the ratio (sin θ) / AD = (sin ACD) / AC.
- Rearranging the formula, we get AC = (AD * sin ACD) / sin θ.
**4. Calculate the width of the river AC:**
- Given that AD = 50 m, θ = 60°, and ACD = 40°, we can substitute these values into the formula.
- AC = (50 * sin 40°) / sin 60°.
- Using trigonometric tables or a calculator, we can find the values of sin 40° and sin 60°.
- Substitute the values and calculate AC.
**5. Simplify the expression and calculate the width:**
- sin 40° ≈ 0.6428
- sin 60° ≈ 0.8660
AC = (50 * 0.6428) / 0.8660
AC ≈ 37.14 / 0.8660
AC ≈ 42.85 m
Therefore, the width of the river AC is approximately 42.85 m.
To find the width of the river AC, we can use the concept of trigonometry and the given information about the bearings and angles.
**1. Draw the given information:**
- Draw a line AB to represent the survey line BAC.
- Mark points A and C on the near and distant banks, respectively.
- Draw a perpendicular line BD from point D to line AB.
- Measure the distance BD as 50 m.
- Label the bearings of C and B as 320° and 230°, respectively.
- Label the angle BDA as θ = 60°.
**2. Determine the angles:**
- Since the bearing of C is 320°, we can determine the angle ACD as 360° - 320° = 40°.
- Similarly, the angle ABD can be determined as 360° - 230° = 130°.
**3. Use trigonometry to find the width of the river:**
- We can use the sine rule to find the width of the river AC.
- The sine rule states that for any triangle ABC, the following ratio holds true: (sin A) / a = (sin B) / b = (sin C) / c.
- In our case, we can use the ratio (sin θ) / AD = (sin ACD) / AC.
- Rearranging the formula, we get AC = (AD * sin ACD) / sin θ.
**4. Calculate the width of the river AC:**
- Given that AD = 50 m, θ = 60°, and ACD = 40°, we can substitute these values into the formula.
- AC = (50 * sin 40°) / sin 60°.
- Using trigonometric tables or a calculator, we can find the values of sin 40° and sin 60°.
- Substitute the values and calculate AC.
**5. Simplify the expression and calculate the width:**
- sin 40° ≈ 0.6428
- sin 60° ≈ 0.8660
AC = (50 * 0.6428) / 0.8660
AC ≈ 37.14 / 0.8660
AC ≈ 42.85 m
Therefore, the width of the river AC is approximately 42.85 m.
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Asurvey line BAC crosses a river as shown in the figure, A and C voids on the near and distant banks, respectively.Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,respectively. The angle BDA equal to theta=60�. What is the width of the river AC? ANS 50/1.732 m?
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Asurvey line BAC crosses a river as shown in the figure, A and C voids on the near and distant banks, respectively.Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,respectively. The angle BDA equal to theta=60�. What is the width of the river AC? ANS 50/1.732 m? 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 Asurvey line BAC crosses a river as shown in the figure, A and C voids on the near and distant banks, respectively.Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,respectively. The angle BDA equal to theta=60�. What is the width of the river AC? ANS 50/1.732 m? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Asurvey line BAC crosses a river as shown in the figure, A and C voids on the near and distant banks, respectively.Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,respectively. The angle BDA equal to theta=60�. What is the width of the river AC? ANS 50/1.732 m?.
Asurvey line BAC crosses a river as shown in the figure, A and C voids on the near and distant banks, respectively.Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,respectively. The angle BDA equal to theta=60�. What is the width of the river AC? ANS 50/1.732 m? 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 Asurvey line BAC crosses a river as shown in the figure, A and C voids on the near and distant banks, respectively.Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,respectively. The angle BDA equal to theta=60�. What is the width of the river AC? ANS 50/1.732 m? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Asurvey line BAC crosses a river as shown in the figure, A and C voids on the near and distant banks, respectively.Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,respectively. The angle BDA equal to theta=60�. What is the width of the river AC? ANS 50/1.732 m?.
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Asurvey line BAC crosses a river as shown in the figure, A and C voids on the near and distant banks, respectively.Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,respectively. The angle BDA equal to theta=60�. What is the width of the river AC? ANS 50/1.732 m?, a detailed solution for Asurvey line BAC crosses a river as shown in the figure, A and C voids on the near and distant banks, respectively.Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,respectively. The angle BDA equal to theta=60�. What is the width of the river AC? ANS 50/1.732 m? has been provided alongside types of Asurvey line BAC crosses a river as shown in the figure, A and C voids on the near and distant banks, respectively.Standing at D, a point 50 m is measured perpendicularly to AB from A. The bearing of C and B are 320� and 230�,respectively. The angle BDA equal to theta=60�. What is the width of the river AC? ANS 50/1.732 m? theory, EduRev gives you an
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