Core Mathematics

1A ladder 10 m long leans against a wall and makes an angle of 60° with the ground. How high up the wall does it reach?

2A man 1.8 m tall stands 20 m from a building and sees its top at an elevation of 40°. Find the height of the building (tan 40° ≈ 0.839).

3Given cos A = −0.5 and 180° ≤ A ≤ 270°, find A.

4The bearing of B from A is 060°. The bearing of A from B is

5If cos θ = 0.6 and θ is acute, find tan θ.

6In which quadrant are both sine and cosine negative?

7If sin x = 0.5 and x is acute, find x.

8Two ships leave a port at the same time; one sails 12 km north, the other 5 km east. How far apart are they?

9Find cos 120°.

10The angle of depression of a boat from a cliff 50 m high is 30°. How far is the boat from the foot of the cliff? (tan 30° ≈ 0.577)