### GCSE Trigonometry paper (H)

#### Year 10/11 maths revision

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

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.

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.

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.

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.

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

ANS

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.

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.

ANS

###### Sine Rule to find an angle  Menu

11. ABC is a triangle CB = 8.5 cm   AC = 6.3 cm   Angle CAB = 63°
Calculate angle CBA of the triangle.

ANS

###### Sine Rule to find a side  Menu

12. ABC is a triangle
CB = 7 cm   Angle CAB = 40 °
Angle ABC = 95 °
Calculate the length of side AC.

ANS

###### Cosine Rule to find a side  Menu

13. ABC is a triangle
AC = 8 cm   AB = 7.5 cm Angle CAB = 45°
Calculate the length of side CB.

ANS

###### Cosine Rule to find an angle  Menu

14. ABC is a triangle
AC = 11.5 cm   AB = 8.8 cm
BC = 6 cm
Calculate angle ACB of the triangle.

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.

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

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.

The base of the pyramid is a regular hexagon with sides of length 4cm. O is the centre.

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
c) Calculate the size of angle GXI Give your answer correct to 3 significant figures

ANS