GCSE Trigonometry paper (H)

Year 10/11 maths revision

Bearings  Menu

1. A plane flies for 200 km on a bearing of 255° from Luton to Cardiff airport.
It lands at Cardiff and then takes off again flying for 225 km on a bearing of 15° to Manchester airport. It then flew back to Luton.
a) Draw luton as a cross at the middle right of a piece of paper. Then using a protractor and ruler make a scale drawing with 25 km = 1 cm.
b) Estimate the bearing and distance (km) from Manchester to Luton.


ANS

Find side of triangle with Tan x  Menu

2. ABC is a right angled triangle.
AB = 10 cm    Angle CAB = 50°
Calculate the length of BC to two dp

trigonometry q2
ANS

Find side of triangle with Cos x  Menu

3. ABC is a right angled triangle.
AB = 9 cm  Angle CAB = 36 °
Calculate the length of AC to two sf.

trigonometry q3
ANS

Find side of triangle with Sin x  Menu

4. ABC is a right angled triangle.
AC = 12 cm   Angle CAB = 58 °
Calculate the length of CB to three sf.

trigonometry q4
ANS

Find angle of triangle with Tan x  Menu

5. A flag pole P is 4.3m W of scout hut H
A camp fire F, is 5.5m N of the flag pole P.
a) Calculate the size of the angle y to 2 sf.

trigonometry q5
ANS

Find angle of triangle with Cos x  Menu

6. ABC is a right angled triangle.
AC = 9 cm   AB = 7 cm
Calculate the angle CAB (x°) to one dp.

trigonometry q6
ANS

Find angle of triangle with Sin x  Menu

7. ABC is a right angled triangle.
AC = 11 cm   CB = 8 cm
Calculate the angle CAB (x°) to two sf


trigonometry q7
ANS

Using Pythagora's theorem  Menu
trigonometry q8

8. WXY is a right angled triangle.
WX = 9 cm   XY = 11 cm
Calculate the length of WY to two dp.


ANS

½absinC to find area of triangle  Menu

9. ABC is a triangle. BC = 11 cm   AC = 5 cm   Angle ACB = 80°
Calculate the area of the triangle.
Give your answer correct to 3 sf.

trigonometry q9
ANS

Find side of triangle from its area  Menu

10. ABC is a triangle with an area of 20cm2
AB = 9.5 cm   Angle ABC = 70°
Calculate the length of side CB.
Give your answer correct to 1 dp

trigonometry q10
ANS

Sine Rule to find an angle  Menu
trigonometry q11

11. ABC is a triangle CB = 8.5 cm   AC = 6.3 cm   Angle CAB = 63°
Calculate angle CBA of the triangle.
Give your answer correct to 1 dp.


ANS

Sine Rule to find a side  Menu
trigonometry q12

12. ABC is a triangle
CB = 7 cm   Angle CAB = 40 °
Angle ABC = 95 °
Calculate the length of side AC.
Give your answer correct to 1 dp.


ANS

Cosine Rule to find a side  Menu
trigonometry q13

13. ABC is a triangle
AC = 8 cm   AB = 7.5 cm Angle CAB = 45°
Calculate the length of side CB.
Give your answer correct to 1 dp.


ANS

Cosine Rule to find an angle  Menu
trigonometry q14

14. ABC is a triangle
AC = 11.5 cm   AB = 8.8 cm
BC = 6 cm
Calculate angle ACB of the triangle.
Give your answer correct to 1 dp.


ANS

Using both Sine and Cosine rules  Menu

15. In the diagram QOP =52°, OQP =60°.
PN = 11 cm, ON = 20 cm and QP = 17 cm.
trigonometry q15
a) Find the length of OP correct to one dp
b) Find the angle ONP correct to one dp
c) Calculate the area of the triangle NOP
Give your answer correct to three sf.

ANS

Find angles between a line and a plane  Menu

16. A pyramid is shown below with apex X.
Each of the sloping edges is 7 cm.
trigonometry q16

The base of the pyramid is a regular hexagon with sides of length 4cm. O is the centre.
trigonometry q16b
a) Calculate the height of X above the base of the pyramid Give your answer to 3 sf.
b) Calculate the size of angle JXG
Give your answer correct to 3 sf.
c) Calculate the size of angle GXI Give your answer correct to 3 significant figures


ANS

Trigonometry Formulae  Menu
formula