Height and Distance Questions

• An observer 1.6 m tall is 20 3 away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The heights of the tower is:
• A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?
• A vertical toy 18 cm long casts a shadow 8 cm long on the ground. At the same time a pole casts a shadow 48 m. long on the ground. Then find the height of the pole ?
• Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:
• Jack takes 20 minutes to jog around the race course one time, and 25 minutes to jog around a second time. What is his average speed in miles per hour for the whole jog if the course is 3 miles long?
• The top and bottom of a tower were seen to be at angles of depression 30° and 60° from the top of a hill of height 100 m. Find the height of the tower ?
• A flagstaff 17.5 m high casts a shadow of length 40.25 m. What will be the height of a building, which casts a shadow of length 28.75 m under similar conditions ?  
• A ladder is resting against a vertical wall and its bottom is 2.5 m away from the wall. If it slips 0.8 m down the wall, then its bottom will move away from the wall by 1.4 m. What is the length of the ladder?
• The height and the slant height of a right circular cone are 24 cm and 25 cm, respectively. Considering π as 22/7 , find the curved surface area of the said cone.
• Two men standing on same side of a pillar 75 metre high, observe the angles of elevation of the top of the pillar to be 30° and 60° respectively the distance between two men is
• There are two parallel streets each directed north to south. A person in the first street travelling from south to north wishes to take the second street which is on his right side. At some place, he makes a 150 deg turn to the right and he travels for 15 minutes at the speed of 20 km/hr. After that he takes a left turn of 60 deg and travels for 20 minutes at the speed of 30 km/hr in order to meet the second street. What is the distance between the two streets?
• The top of a broken tree touches the ground at a distance of 15 m from its base. If the tree is broken at a height of 8 m from the ground, then the actual height of the tree is
• A ladder 13 m long reaches a window which is 12 m above the ground on side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to each a window 5m high, then the width of the street is :
• From a point P on a level ground , the angle of elevation to the top of the tower is 30° . If the tower is 100m high , the distance of point P from the foot of the tower is ( Take √3 = 1.73)
• A tower is broken at a point P above the ground. The top of the tower makes an angle 60° with the ground at Q. From another point R on the opposite sideof Q angle of elevation of point P is 30°. If QR = 180 m, then what is the total height (in metres) of the tower?
• On a ground , there is a vertical tower with a flagpole on its top . At a point 9 m away from the foot of the tower , the angles of elevation of the top and bottom of the flagpole are 60° and 30° respectively . The height of the flagpole is
• Two ships are sailing in the sea on the two sides of a light house. The angle of elevation of the top of the light house as observed from the two ships are 30° and 45° respectively. If the light house is 100m high, the distance between the two ships is :(take √3=1.73)
• A man standing on the bank of river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 36 m from the bank, he finds that the angle is 30°. The breadth of the river is
• A kite is flying in the sky. The length of string between a point on the ground and kite is 420 m. The angle of elevation of string with the ground is 30 deg. Assuming that there is no slack in the string, then what is the height (in metres) of the kite?
• Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angle of depressions of the point from the top of the trees are 45 deg and 60 deg. If the height of the tree which makes 45 deg angle is 200 metres, then what will be the height (in metres) of the other tree?