MEDIUM
JEE Main
IMPORTANT
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The angle of elevation of the top of a tower from a point due north of it is and from a point at a distance of units due west of is . If the distance of the point from the tower is units, then is equal to
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Important Questions on Heights and Distances
EASY
JEE Main
IMPORTANT
A vertical pole fixed to the horizontal ground is divided in the ratio by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground away from the base of the pole, then the height of the pole (in meters) is :
MEDIUM
JEE Main
IMPORTANT
A spherical gas balloon of radius meter subtends an angle at the eye of the observer while the angle of elevation of its center from the eye of is . Then the height (in meter) of the top most point of the balloon from the level of the observer's eye is :
HARD
JEE Main
IMPORTANT
A pole stands vertically inside a triangular park . Let the angle of elevation of the top of the pole from each corner of the park be . If the radius of the circumcircle of is , then the height of the pole is equal to :
MEDIUM
JEE Main
IMPORTANT
Two vertical poles are apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is:
MEDIUM
JEE Main
IMPORTANT
The angle of elevation of a jet plane from a point on the ground is After a flight of seconds at the speed of , the angle of elevation changes to If the jet plane is flying at a constant height, then its height is:
MEDIUM
JEE Main
IMPORTANT
A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point , with uniform speed. At that point, angle of depression of the boat with the man's eye is (Ignore man's height). After sailing for seconds, towards the base of the tower (which is at the level of water), the boat has reached a point , where the angle of depression is Then the time taken (in seconds) by the boat from to reach the base of the tower is :
HARD
JEE Main
IMPORTANT
The angle of elevation of a cloud from a point above a still lake is . If the angle of depression of the image of in the lake from the point is , then (in ) is equal to
HARD
JEE Main
IMPORTANT
The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be . After walking a distance of meters towards the top, up a slope inclined at angle of to the horizontal plane the angle of elevation of the top of the hill becomes . Then the height of the hill (in meters) is _____.
