Practice Height and Distance Questions and Answers

• A man 3 m tall is 23 m away from a tower 26 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.
• A man 2 m tall is 25 m away from a tower 27 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.
• If distance between two pillars of length 16 & 9 cm is x cm. If two angle of elevation of their respective top from a point on ground of other are comp...
• The length of the shadow of a vertical tower increases by 8 m on horizontal ground when the height of the sun changes from 45° to 30 ° , then find the he...
• The length of the shadow of a vertical tower increases by 9 m on horizontal ground when the height of the sun changes from 45° to 30 ° , then find ...
• The angle of elevation of the top of a building from the foot of a tower is 30° and the angle of elevation of the top of the tower from the foot of the bu...
• The angle of depression of a point on the ground as seen from the top of a tower, 35 feet high, is 45°. Find the distance of the point on the ground from ...
• The angle of depression of a point on the ground as seen from the top of a tower, 20 feet high, is 45°. Find the distance of the point on the ground from ...
• The angle of depression of a point on the ground as seen from the top of a tower, 65 feet high, is 45°. Find the distance of the point on the ground from ...
• There are two houses of the same height on both sides of a 15-meter wide road. From a point on the road, elevation angles of the houses are 30° and 60° r...
• There are two houses of the same height on both sides of a 30-meter wide road. From a point on the road, elevation angles of the houses are 30° and 60&...
• There are two houses of the same height on both sides of a 40-meter wide road. From a point on the road, elevation angles of the houses are 30° and 60° r...
• A boat is being rowed away from a cliff 240 m high. From the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 3 min...
• A boat is being rowed away from a cliff 270 m high. From the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 2 minutes. ...
• A boat is being rowed away from a cliff 183 m high. From the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 3 minutes. ...
• The angle of elevation of an aeroplane from a point on the ground is 60°. After 20 seconds flight the elevation changes to 30°, if the aeroplane is...
• 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 elev...
• A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of th...
• From the top of a lighthouse, the angle of depression to the top and bottom of a tower is 30° and 45°, respectively. If the lighthouse is 210 metre...
• A man whose height is 1.5 metres is standing 24√3 metres away from a light pole. The angle of elevation from his head to the top of the light pole is...
• A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle of 30° with the ground. The distance ...
• From 110m high towers, the angle of depression of a car is 45°. Then how far the car is from the tower?
• A pole got broken by the wind whose top meets the ground at an angle of 30° at a distance of 45 meters from the foot. What was the total height of the ...
• At a point 20 metres away from the base of a 20√3, metres high house, the angle of elevation of the top is 
• From a point situated at some distance from the base of a pillar, the angle of elevation of the top of the pillar is found to be 45 degrees. After walking ...
• From the top of an upright pole 30√3 feet high, the angle of elevation to the top of an upright tower was 60°. If the foot of the pole was 55 feet away ...
• Two ships are on opposite sides in front of a lighthouse in such a way that all three of them are in line. The angles of depression of two ships from the t...
• From a watch tower of 205 m height, the angles of depression of two cliffs in a horizontal line through the base of the tower are 45° and 30°. Find the d...
• Find the angle of elevation of a 125 √ 3m tower's top from a point 125 m away from its base.
• A tree breaks due to a storm and the top touches the ground 30 meters away from its base, making a 30-degree angle with the ground. What was the height of ...
• The two buildings are 100m apart. From the top of the first building, which is 60m tall, the angle of depression to the top of the second building is 45 de...
• From the top of a straight pillar 20 meters high, the angle of elevation of the top of a straight tower was 45°. If the tower was 70 meters high, then at ...
• Now a chord of a circle is such that AB = 10 cm. If the diameter of the circle is 20 cm, then the angle subtended by the chord at the center is.
• The shadow of a pole on ground level is increased by 24 m when the angle of depression of the sun changes from 60° to 30°. What is the height of the pole...
• The angle of elevation of a ladder leaning against a wall is 60°  and the foot of the ladder is 5 m away from the wall. The length of the ladder
• Find the angle of elevation of a 100m tower's top from a point 100 √ 3m away from its base.
• Due to a cyclone, a tree is broken and makes an angle of 30º with the ground. The distance between the root and the tip of the tree that touches the groun...
• From a watch tower of 150 m height, the angles of depression of two cliffs in a horizontal line through the base of the tower are 45° and 30°. Find the d...
• A long metallic cable is stretched from a point P on the ground to the top of a cliff, forming an angle of 30 ° with the horizontal ground. The total leng...
• Rohit is climbing on a 30 metres long rope, which is tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by t...