IGCSE Maths Trigonometry topical questions

Use Pythagoras’ theorem.

1. (a)A right-angled triangle has legs 6 cm and 8 cm. Find the hypotenuse.[2]
2. (b)A right-angled triangle has hypotenuse 13 cm and one leg 5 cm. Find the other leg.[2]

A ramp rises 1.8 m over a horizontal distance of 6.5 m.

1. (a)Write down an equation for the angle θ the ramp makes with the ground.[2]
2. (b)Find θ, giving your answer to 1 decimal place.[2]

A tent pole stands 2.4 m vertically. A rope runs from the top of the pole to a peg on the ground 1 m from the base.

1. (a)Find the length of the rope.[2]
2. (b)Work out the angle between the rope and the ground, to 1 decimal place.[2]
3. (c)Write down the angle the rope makes with the pole.[1]

A zip wire drops 9.5 m vertically while descending at 28° to the horizontal.

1. (a)Write down the trigonometric ratio needed to find the length of the wire.[1]
2. (b)Find the length of the wire, to 3 significant figures.[2]
3. (c)A steeper zip wire drops the same 9.5 m at 42°. Find its length, to 3 significant figures.[2]

From the top of a cliff 40 m high, a boat is seen at an angle of depression of 25°. (Extended)

1. (a)Write down the angle of elevation of the cliff top from the boat, giving a reason.[1]
2. (b)Find the horizontal distance of the boat from the foot of the cliff, to 3 significant figures.[2]
3. (c)Find the direct distance from the cliff top to the boat, to 3 significant figures.[2]

Use exact values. (Extended)

1. (a)Evaluate sin 30° + cos 60°.[1]
2. (b)Evaluate tan 45° × sin 60°.[2]
3. (c)Solve cos x = √2⁄2 for 0° ⩽ x ⩽ 360°.[2]

A flagpole casts a 15 m shadow when the sun’s elevation is 36°.

1. (a)Find the height of the flagpole, to 3 significant figures.[2]
2. (b)Later in the day the shadow shortens to 8 m. Find the new elevation of the sun, to 1 decimal place.[3]

In triangle ABC, angle A = 74°, angle B = 49° and a = 12 cm. (Extended)

1. (a)Find angle C.[1]
2. (b)Find the length of b, giving your answer to 3 s.f.[3]
3. (c)Find the length of c, giving your answer to 3 s.f.[2]

In triangle PQR, angle P = 40°, QR = 6 cm and PR = 9 cm. (Extended)

1. (a)Write down the sine rule for this triangle.[1]
2. (b)Find the acute value of angle Q, to 1 decimal place.[2]
3. (c)Explain why angle Q could also be obtuse, and state that value.[2]

In triangle ABC, AB = 8 cm, AC = 11 cm and angle BAC = 55°. (Extended)

1. (a)Find BC, to 3 significant figures.[3]
2. (b)Find the area of the triangle, to 3 significant figures.[2]
3. (c)Hence find the shortest distance from A to the line BC, to 3 significant figures.[1]

A cuboid measures 3 cm by 4 cm by 12 cm. (Extended)

1. (a)Show that the diagonal of the 3 cm × 4 cm face is 5 cm.[1]
2. (b)Find the space diagonal of the cuboid.[3]
3. (c)Find the angle between the space diagonal and the base plane, to 1 decimal place.[2]

In triangle XYZ, XY = 7 cm, YZ = 9 cm and ZX = 11 cm. (Extended)

1. (a)Find the largest angle of the triangle, to 1 decimal place.[4]
2. (b)Find the area of the triangle, to 3 significant figures.[3]

A cuboid measures 8 cm by 5 cm by 10 cm. (Extended)

1. (a)Find the length of the diagonal of the 8 cm by 5 cm base, to 3 significant figures.[2]
2. (b)Find the space diagonal of the cuboid, to 3 significant figures.[2]
3. (c)Find the angle the space diagonal makes with the base, to 1 decimal place.[3]

In triangle ABC, AB = 9 cm, AC = 13 cm and angle BAC = 72°. (Extended)

1. (a)Find BC, to 3 significant figures.[3]
2. (b)Find angle ABC, to 1 decimal place.[3]
3. (c)Find the area of the triangle, to 3 significant figures.[1]