Trigonometry Height Distance Bearing 10 Application Examples

Trigonometry Review: https://www.youtube.com/watch?v=-b_74C4ioG4&list=PLJ-ma5dJyAqqEv5UpYmUFj6PVyMpHrLZ6&index=2
Q1. The angle of elevation of the top of the tree from a distance of 40 m from its foot is 30˚. Find the height of the tree.

Q2. The angle of elevation of the top of the tree from the eye level of an observer, 1.6 m tall is 50˚. Find the height of the tree if the the observer is 60 m away from the tree.

Q3. A light house is 100 m above the sea level. The angle of depression of a ship sailing directly towards it changes from 30˚ to 60˚. Find the distance traveled by the ship.

Q4. A ladder inclined at an angle of 60˚ to the horizontal reaches 3 m short of the top of a tree. Find the length of the ladder if the tree is 10 m high.

Q5. The angle of elevation of the top of a tree from points A and B is 60˚ and 40˚ respectively. Find the height of the tree if the distance AB is 6 m. Assume A and B on the same side of the tree.

Q6. The angle of elevation of the top of a building from the top and bottom of a tree is 20˚ and 60˚ respectively. Find the height of the building if the tree is 12m high.

Q7. The angle of elevation of the top of a building from the foot of the tower is 30˚ and the angle of elevation of the tower is 60˚ from the foot of the bukding. If the tower is 40 m heigh find the height of the building.

Q8. The angle of elevation to the top of the tower is 32˚ from a point A due south of it. The angle of elevation to the top of the tower from another point B due west of the tower is 40˚. Find the height of the tower if the distance AB is 45 m.

Q9. A ship sails 25 km from A at a bearing of 036˚ to reach B. Then it moves to port C, 45 km away at a bearing of 090˚. What is the distance and bearing of C from A?

Q10. A ship sails 60 km from A at a bearing of 130˚, then further 150 km on a bearing of 220˚ and then returns directly to the starting point. Find the length and the bearing of the return journey.