**Height and Distance Worksheet**
**Instructions:**
1. Solve all the problems.
2. Show your work and calculations where necessary.
3. Circle or underline your final answers.
**Easy Problems:**
1. A flagpole stands vertically on the ground. If the angle of elevation to the top of the flagpole is 45 degrees and you are standing 20 meters away from the flagpole, find the height of the flagpole.
2. From the top of a building 30 meters high, the angle of depression of an object on the ground is 60 degrees. Find the distance of the object from the base of the building.
3. If the length of a shadow of a 10-meter pole is 8 meters, find the angle of elevation of the sun.
4. A ladder leans against a wall. The angle of elevation of the ladder is 60 degrees, and the ladder reaches a height of 10 meters on the wall. Find the length of the ladder.
5. Two ships are sailing towards each other. They spot each other when they are 1,000 meters apart, and the angle of elevation is 30 degrees from one ship to the other. Find the altitude of each ship.
**Medium Problems:**
6. A 15-meter ladder is leaning against a wall. If the ladder makes a 45-degree angle with the ground, how far is the bottom of the ladder from the wall?
7. A person standing 50 meters away from a tree finds that the angle of elevation to the top of the tree is 30 degrees. Find the height of the tree.
8. An observer on a cliff sees a boat in the sea below at an angle of depression of 45 degrees. If the cliff is 60 meters high, find the distance between the boat and the observer.
9. A 12-meter ladder is placed against a wall. If the top of the ladder slides down the wall at a rate of 2 meters per second, how fast is the bottom of the ladder moving away from the wall when the top of the ladder is 9 meters above the ground?
10. Two buildings are 100 meters apart. From the top of one building, the angle of elevation to the top of the other is 30 degrees. If the height of the first building is 40 meters, find the height of the second building.
**Difficult Problems:**
11. From a point 15 meters above the water surface, the angle of elevation of a cliff is 60 degrees. If the cliff is 15 meters from the shore, find the depth of the water.
12. An airplane is flying at an altitude of 5,000 meters. An observer on the ground sees the airplane at an angle of elevation of 30 degrees. Find the horizontal distance between the observer and the airplane.
13. Two towers are 100 meters apart. From the top of the first tower, the angle of elevation to the top of the second tower is 45 degrees. If the height of the first tower is 60 meters, find the height of the second tower.
14. A man stands on the top of a hill and sees a car coming towards him. If the angle of depression of the car is 30 degrees when it is 300 meters away, find the height of the hill.
15. A 20-meter ladder leans against a wall. If the ladder makes an angle of 75 degrees with the ground, find the height at which the ladder touches the wall.
**Answers:**
**Easy Problems:**
1. 20 meters
2. 30 meters
3. 60 degrees
4. 20 meters
5. Altitude of each ship is 500 meters.
**Medium Problems:**
6. 15 meters
7. 25 meters
8. 60 meters
9. 2 m/s
10. 20 meters
**Difficult Problems:**
11. 15 meters
12. 10,000 meters (10 km)
13. 60 meters
14. 150 meters
15. 5√3 meters
