1.
In the diagram below, a diver is to retrieve an object that is 14m away from the wall of a swimming pool. It is given that the angle of depression of the object from the pool platform is 30°. Find the vertical distance the diver has to swim in order to retrieve the object, correct to 3 significant figures.
2.
Using the diagram below, determine the angle of elevation of the top of the flagpole 10m high from an observer who is 10m away from the flagpole.
3.
Using the diagram below, find the angle of elevation of a kite on a 50m string flying 40m vertically above the ground. Correct the answer to 1 decimal place.
4.
A skier took 56s to traverse down the snowy slopes of a 300m high hill. Using the diagram below, if the skier traversed from point S to point U and the angle of depression from S to U is 60°, find the speed, in km/h, at which he came down the slopes. Correct the answer to 3 significant figures.
5.
Man A fixes some wire on the ground to the top of a 2.25m pole at an angle of elevation of 40°. Man B fixes some wire as well but at the opposite end of man A and at an angle of elevation of 60°. Express as a percentage, the length of wire used by man B to the total length of wire used by both men, correct to 3 significant figures.
6.
A 1.8m tall man is walking inside a tunnel. He shines the torchlight on his helmet upward at an angle of 35° to a point Q at the top of the tunnel as shown in the diagram below. Given that the horizontal distance of OP is 7m, what is the height of the tunnel, correct to 3 significant figures?
7.
In the diagram below, a closed-circuit security camera, C, in a museum is mounted on a wall 9m above the floor, G. What is the angle of depression of the exhibit, E, from C, given that E is 2m above the floor, H, and 12m from the wall? Correct the answer to 1 decimal place.
8.
In the diagram below, an aeroplane, P, cruising at an altitude of 10km begins its landing at Changi Airport, denoted by C, at an angle of depression of 10°.a) Find the horizontal distance between the aeroplane and Changi Airport when the aeroplane begins its landing, correct to 3 significant figures.b) Hence, find the distance CP, correct to 3 significant figures.
9.
In the diagram below, buildings P and Q are 50m apart. The angle of elevation of T from R is 53° and the angle of depression of V from R is 41°. Determine the height TV of building Q, correct to 3 significant figures.
10.
In the diagram below, OP is a painting hung on a wall OQ. S and R are points on the level ground such that OR = PS = 8m. The angle of elevation of the top frame, O, of the painting from R is 58° while that of lower frame, P, of the painting from S is 33°. Find the height of the painting, correct to 3 significant figures.