Height and Distance Questions

• A Navy captain going away from a lighthouse at the speed of 4[(√3) – 1] m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from 60 to 45 deg. What is the height (in metres) of the lighthouse?
• From the top of a tower 60 mts high the angle of depression of the top and bottom of a pole are observed to be 45° and 60° respectively. If the pole and tower stand on the same plane, the height of the pole in meters is
• If the elevation of the Sun changes from 30° to 60° , then the difference between the lengths of shadows of a pole 15 m high, is
• 129 meter from the foot of a cliff on level of ground, the angle of elevation of the top of a cliff is 30°. The height of this cliff is
• A tower is 50 meters high.Its shadow is x metres shorter when the sun's altitude is 45° than when it is 30° . The value of x in metres is
• The length of shadow of a tower is √3 times that of its length. The angle of elevation of the sun is
• Two persons are on either side of a temple, 75 m high, observe the angle of elevation of the top of the temple to be 30 and 60 deg respectively. The distance between the persons is
• From the top of a 20 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of it's foot is at 45°, then the height of the tower is (√3=1.732)
• The angle of elevation of a ladder leaning against a wall is 60 deg and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is
• The upper part of a tree broke at a certain height makes an angle of 60 ° with the ground at a distance of 10 m. from its feet. The original height of the tree was
• A boat is moving away from an observation tower. It makes an angle of depression of 60° with an observer's eye when at a distance of 50m from the tower. After 8 sec., the angle of depression becomes 30°. By assuming that it is running in still water, the approximate speed of the boat is
• The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, then the speed of the aeroplane in km/hr. is
• The shadow of a tower when the angle of elevation of the sun is 45°, is found to be 10 m longer than when it was 60° . The height of the tower is
• Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30 ̊ and 45 ̊ respectively. If the height of the tower is 50 m, the distance between the two men is (Take √3 = 1.73)
• A 25m long ladder is rested on a wall. The foot of the ladder is 7m away from the wall. If the end of the ladder (resting on the wall) slides down 4m, then how far will its foot move away?
• The angles of elevation of top and bottom of a flag kept on a flag post from 30 metres distance, are 45 and 30 deg respectively. Height of the flag is [taking √3 = 1.732]
• A pilot in an aeroplane at an altitude of 200 m observes two points lying on either side of a river. If the angles of depression of the two points be 45° and 60°, then the width of the river is
• A telegraph post is bent at a point above the ground. Its top just touches the ground at a distance of 8√3 m from its foot and makes an angle of 30° with the horizontal. The height (in metre) of the post is
• The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is
• A helicopter, at an altitude of 1500 m, finds that two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are 60° and 30°respectively. Distance between the two ships, in metres is