A ladder is leaning against a wall where the upper end is 4.5 m high from the ground. The angle of inclination of the ladder to the ground is . Find the length of the ladder giving the answer to two decimal places.
A building is 8.78 km tall from the ground. The angle of elevation of the top of the building from a point on the ground is . Find the distance between the point on the ground and the top of the building giving the answer to the nearest metre.
A passenger on a ship gazes towards the mountainous shore and notices that, from where he stands, the summit of one mountain lies directly behind the summit of another; both summits are west of north from him. 4 hours later, he looks for the two mountains again, and finds that they no longer line up; one is south of west from him and the other is north of west. Given that the ship he is on was travelling northeast at a speed of 34 km/h, find the distance between the two mountains.