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From a point P on a level ground, the angle of elevation of the top of a tower is 30 degrees. If the tower is 100 m high, the distance of point P from the foot of the tower is:
- a)149 m
- b)156 m
- c)173 m
- d)200 m
- e)220 m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
From a point P on a level ground, the angle of elevation of the top of...
Let QR be the tower. Then,
QR = 100 m and angle QPR = 30 degrees.
We know, cot 30° = √3 = PQ/QR.
Therefore, PQ = 100*√3 = 173 m.
QR = 100 m and angle QPR = 30 degrees.
We know, cot 30° = √3 = PQ/QR.
Therefore, PQ = 100*√3 = 173 m.
Most Upvoted Answer
From a point P on a level ground, the angle of elevation of the top of...
To solve this question, we can use trigonometry. Let's break down the problem into smaller parts:
1. Drawing the diagram:
- Draw a line segment representing the height of the tower.
- From point P, draw a line segment representing the distance from the foot of the tower to point P.
- Label the angle of elevation as 30 degrees.
- Label the height of the tower as 100 m.
2. Identifying the trigonometric relationship:
- The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
- In this case, the opposite side is the height of the tower (100 m) and the adjacent side is the distance from the foot of the tower to point P (unknown).
- Therefore, we can use the tangent function to solve for the distance from the foot of the tower to point P.
3. Applying the tangent function:
- The tangent of an angle can be calculated using the formula: tan(angle) = opposite/adjacent.
- In this case, tan(30 degrees) = 100 m/adjacent.
- Rearranging the equation, we get: adjacent = 100 m/tan(30 degrees).
4. Calculating the distance from the foot of the tower to point P:
- Using a calculator, we can find that tan(30 degrees) is approximately 0.577.
- Substituting this value into the equation, we get: adjacent = 100 m/0.577.
- Solving for adjacent, we find that the distance from the foot of the tower to point P is approximately 173 m.
Therefore, the correct answer is option C) 173 m.
1. Drawing the diagram:
- Draw a line segment representing the height of the tower.
- From point P, draw a line segment representing the distance from the foot of the tower to point P.
- Label the angle of elevation as 30 degrees.
- Label the height of the tower as 100 m.
2. Identifying the trigonometric relationship:
- The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
- In this case, the opposite side is the height of the tower (100 m) and the adjacent side is the distance from the foot of the tower to point P (unknown).
- Therefore, we can use the tangent function to solve for the distance from the foot of the tower to point P.
3. Applying the tangent function:
- The tangent of an angle can be calculated using the formula: tan(angle) = opposite/adjacent.
- In this case, tan(30 degrees) = 100 m/adjacent.
- Rearranging the equation, we get: adjacent = 100 m/tan(30 degrees).
4. Calculating the distance from the foot of the tower to point P:
- Using a calculator, we can find that tan(30 degrees) is approximately 0.577.
- Substituting this value into the equation, we get: adjacent = 100 m/0.577.
- Solving for adjacent, we find that the distance from the foot of the tower to point P is approximately 173 m.
Therefore, the correct answer is option C) 173 m.
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From a point P on a level ground, the angle of elevation of the top of a tower is 30 degrees. If the tower is 100 m high, the distance of point P from the foot of the tower is:a)149 mb)156 mc)173 md)200 me)220 mCorrect answer is option 'C'. Can you explain this answer?
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From a point P on a level ground, the angle of elevation of the top of a tower is 30 degrees. If the tower is 100 m high, the distance of point P from the foot of the tower is:a)149 mb)156 mc)173 md)200 me)220 mCorrect answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about From a point P on a level ground, the angle of elevation of the top of a tower is 30 degrees. If the tower is 100 m high, the distance of point P from the foot of the tower is:a)149 mb)156 mc)173 md)200 me)220 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a point P on a level ground, the angle of elevation of the top of a tower is 30 degrees. If the tower is 100 m high, the distance of point P from the foot of the tower is:a)149 mb)156 mc)173 md)200 me)220 mCorrect answer is option 'C'. Can you explain this answer?.
From a point P on a level ground, the angle of elevation of the top of a tower is 30 degrees. If the tower is 100 m high, the distance of point P from the foot of the tower is:a)149 mb)156 mc)173 md)200 me)220 mCorrect answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about From a point P on a level ground, the angle of elevation of the top of a tower is 30 degrees. If the tower is 100 m high, the distance of point P from the foot of the tower is:a)149 mb)156 mc)173 md)200 me)220 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a point P on a level ground, the angle of elevation of the top of a tower is 30 degrees. If the tower is 100 m high, the distance of point P from the foot of the tower is:a)149 mb)156 mc)173 md)200 me)220 mCorrect answer is option 'C'. Can you explain this answer?.
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