Height and Distance Questions

• From the top of a lighthouse, 50 m above the sea, the angle of depression of an incoming boat is 30°. How far is the boat from the lighthouse?
• On the level ground, the angle of elevation of the top of the tower is 30°. On moving 20 m nearer, the angle of elevation is 60°. The height of the tower is :
• Angle of depression from the top of a lighthouse of two boats are 45° and 30° due east which are 60 m apart. The height of the light house is :
• If a flag staff of 6 m height placed on the top of a tower throws a shadow of 2 √3 m along the ground, then the angle that the sun makes with the ground is :
• The angle of elevation of the top of a TV tower from three points A, B, C in a straight line through the foot of the tower are α, 2α, 3α, respectively. If AB = a, the height of the tower is :
• A man is standing on the 8 m long shadow of a 6 m long pole. If the length of the shadow is 2.4 meter, then the height of the man is :
• A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 60 meter from the tower. After 5 second, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming it is running in still water?
• From the top of a tower of height 108 meter the angles of depression of two objects on either sides of the tower are 30° and 45°. The distance between the objects are :
• ABCD is a rectangle where the ratio of the lengths of AB and BC is 3 : 2. If P is the midpoint of AB, then the value of sin (∠CPB) is :
• The angles of elevation of the top of a tower from the points P and Q, at distances of 'a' and 'b' respectively from the base of the tower and in the same straight line with it are complementary. The height of the tower is :
• The length of a shadow of a vertical tower is 1 √3 times of its height. The angle of elevation of the Sun is :
• If an object travels at five feet per second, how many feet does it travel in one hour?
• 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 ?
• 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?
• 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 ?  
• The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
• 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.