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As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once
there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the
help of a rope which normal board electricians were carrying on bicycles.
This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o
with line AC.
What is value of angle PBC?
there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the
help of a rope which normal board electricians were carrying on bicycles.
This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o
with line AC.
What is value of angle PBC?
Most Upvoted Answer
As shown In the village of Surya there was a big pole PC. This pole wa...
Understanding the Problem
In the village of Surya, a pole PC is tied with a wire of length 10 m. Electricians need a staircase that reaches point P on the pole, forming a 60° angle with line AC. The goal is to determine the angle PBC.
Visualizing the Scenario
- **Pole and Wire Setup:**
- The pole PC is vertical.
- The wire of length 10 m is used to reach point P at an angle of 60° with AC.
- **Triangle Formation:**
- The triangle formed is PBC, where:
- P is the point on the pole.
- B is the base where the staircase touches the ground.
- C is the point at the bottom of the pole.
Using Trigonometry
To find angle PBC, we can employ trigonometric relationships in triangle PBC. Given that the wire makes a 60° angle with line AC:
- **Side Lengths:**
- Length of wire (hypotenuse) = 10 m.
- Angle APC (between wire and pole) = 90° - 60° = 30°.
- **Calculating Sides:**
- Using the sine function:
- \( PB = 10 \times \sin(30°) = 10 \times 0.5 = 5 \, m \) (vertical height)
- Using the cosine function:
- \( BC = 10 \times \cos(30°) = 10 \times \frac{\sqrt{3}}{2} \approx 8.66 \, m \) (horizontal distance)
Finding Angle PBC
In triangle PBC:
- Since we have the opposite side (PB) and the adjacent side (BC), we can find angle PBC using the tangent function:
- \( \tan(PBC) = \frac{PB}{BC} = \frac{5}{8.66} \)
- Calculate angle PBC:
- \( PBC = \tan^{-1}\left(\frac{5}{8.66}\right) \)
- Approximate value of PBC ≈ 30°.
Conclusion
Thus, the value of angle PBC is approximately 30°. This analysis shows how trigonometric principles can effectively solve practical problems in real-life scenarios.
In the village of Surya, a pole PC is tied with a wire of length 10 m. Electricians need a staircase that reaches point P on the pole, forming a 60° angle with line AC. The goal is to determine the angle PBC.
Visualizing the Scenario
- **Pole and Wire Setup:**
- The pole PC is vertical.
- The wire of length 10 m is used to reach point P at an angle of 60° with AC.
- **Triangle Formation:**
- The triangle formed is PBC, where:
- P is the point on the pole.
- B is the base where the staircase touches the ground.
- C is the point at the bottom of the pole.
Using Trigonometry
To find angle PBC, we can employ trigonometric relationships in triangle PBC. Given that the wire makes a 60° angle with line AC:
- **Side Lengths:**
- Length of wire (hypotenuse) = 10 m.
- Angle APC (between wire and pole) = 90° - 60° = 30°.
- **Calculating Sides:**
- Using the sine function:
- \( PB = 10 \times \sin(30°) = 10 \times 0.5 = 5 \, m \) (vertical height)
- Using the cosine function:
- \( BC = 10 \times \cos(30°) = 10 \times \frac{\sqrt{3}}{2} \approx 8.66 \, m \) (horizontal distance)
Finding Angle PBC
In triangle PBC:
- Since we have the opposite side (PB) and the adjacent side (BC), we can find angle PBC using the tangent function:
- \( \tan(PBC) = \frac{PB}{BC} = \frac{5}{8.66} \)
- Calculate angle PBC:
- \( PBC = \tan^{-1}\left(\frac{5}{8.66}\right) \)
- Approximate value of PBC ≈ 30°.
Conclusion
Thus, the value of angle PBC is approximately 30°. This analysis shows how trigonometric principles can effectively solve practical problems in real-life scenarios.
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As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. What is value of angle PBC?
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As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. What is value of angle PBC? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. What is value of angle PBC? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. What is value of angle PBC?.
As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. What is value of angle PBC? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. What is value of angle PBC? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. What is value of angle PBC?.
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