A man is standing at point A watching the top of the building making an angle of elevation of 30°. He walks towards the building and stopped at point P at a distance of 20m and the angle of elevation becomes 60°. What is the distance between the foot of the building and point P?
10 m
Let d be the distance from P to the foot of the building and h the height. From P: tan60° = h/d, so h = d√3. From A: tan30° = h/(d+20), so h = (d+20)/√3. Equating the two gives 3d = d + 20, so d = 10 m. Note: the mark on this item in the source paper did not match this standard calculation, so it is flagged for review.
Important Questions from Heights and Distances
If x is the distance of P from the bottom of the pillar, then consider the following statements :
1. x can take two values which are in the ratio 1 : 3
2. x can be equal to the height of the flagstaff
Which of the statements given above is/are correct?
What is a possible value of tan θ ?
A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. From a point on the field, the angles of elevation of the bottom and tip of the flag staff are 30° and 45° respectively. Which one of the following gives the best approximation to the height of the tower?
Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15° with the horizontal. The distance between the poles is approximately equal to
The angle of elevation of the top of a tower from a point 20 m away from its base is 45 °. What is the height of the tower?
