**(1)** A tree is broken at a certain height and its top touches the ground at a distance of 12 meters from its base. If the tree is broken at a height of 5 meters from the ground, what was the original height of the tree?

- (a) 12 meters
- (b) 13 meters
- (c) 17 meters
- (d) 18 meters

**(2)** From the top of a building 20 meters high, the angle of depression to a car on the ground is observed to be 30 degrees. How far is the car from the base of the building?

- (a) 10√3 meters
- (b) 20 meters
- (c) 20√3 meters
- (d) 40 meters

**(3)** An observer 1.6 meters tall is \( 20\sqrt{3} \) meters away from a tower and observes the angle of elevation to the top of the tower to be 60 degrees. What is the height of the tower?

- (a) 18.4 meters
- (b) 20 meters
- (c) 34.6 meters
- (d) 38.4 meters

**(4)** A person observes a tower at an angle of elevation of 30°. Moving 40 meters closer, the angle of elevation increases to 45°. What is the initial distance from the person to the base of the tower?

- (a) 40(√3 – 1) meters
- (b) 40√3 meters
- (c) 80 meters
- (d) 40√2 meters

**(5)** From the top of a cliff 150 meters high, the angle of depression of a boat is 30 degrees. How far is the boat from the foot of the cliff?

- (a) 150√3 meters
- (b) 150 meters
- (c) 150/√3 meters
- (d) 300 meters