1
1. Shown below is a right-angled triangle.
Use trigonometry to work out the size of angle x.
.................°
(3)
2.
Work out the size of angle x
2
.................°
(3)
3
3. ABC is a right-angled triangle
Work out the size of the angle marked x.
.
.................
°
(3)
4. Below is a right-angled triangle.
(3)
Use trigonometry to work out the length x.
.
.................
cm
(3)
5.
Work out the length x.
.................cm
(3)
6.
Work out the length of RT.
(3)
.................cm
(3)
7. Triangle ABC has a right
angle. Angle BAC is 25°
AC = 12.5cm
Calculate the length of AB
.................cm
(3)
8. DEF is a right-angled triangle.
Calculate the size of angle DEF.
(3)
.................°
(3)
9.
Work out the length of side x.
Include suitable units.
....................
(3)
10. Shown is a right-angled triangle
sin30∘ = 0.5
(3)
Work out the value of x
....................
(3)
11. A ladder is placed against a vertical wall.
To be safe, it must be inclined at between 70° and 80° to the ground.
(a) Is the ladder safe?
.........................
(3)
(b)Calculate the length of the ladder.
.....................m
(3)
12. A ramp is built to help people enter a building.
The start of the ramp is 2.1 metres from the base of the
building. The ramp has a height of 20 centimetres.
Calculate the size of angle y.
.
.................
°
(3)
13. Shown below is right-angled triangle DEF.
Angle E is 12° larger than
angle D Work out the length of
DE.
.
.................
cm
(4)
14. The diagram shows two right-angled triangles.
Calculate the value of x.
.
.....................
cm
(5)
15. Two right-angled triangles are shown
below. AB is 10cm
BC is 3cm
Angle BCD is 65°
Calculate the size of angle ABD
.
.................
°
(5)
16. The diagram shows a right-angled triangle.
Calculate the length of side x.
.
.....................
cm
(3)
17. ABC is a right-angled triangle.
anx = 0.6
Work out the length of BC
.
.....................
cm
(3)
18. Shown below are right-angled triangles, ABD and BCD.
AB = 15cm
Angle ABD = 70°
Angle ABD : Angle DBC = 5 : 2
Work out the length of CD
.
.....................
cm
(5)
19. ABCD is a rectangle.
BD = 9cm
Angle BDC = 40°
(a) Work out the length of BC
.
.....................
cm
(2)
(b) Work out the perimeter of rectangle ABCD
.
.....................
cm
(3)
20. Shown below is a parallelogram.
Calculate the area of the parallelogram.
.
.....................
cm²
(5)
21. A regular hexagon can be divided into 6 equilateral
triangles. The diagram below shows one of the
equilateral triangles.
(a) Use trigonometry to find the height, x, of the equilateral triangle.
.
.....................
cm
(3)
(b)Calculate the area of the equilateral triangle.
.
....................
cm²
(1)
(c) Calculate the area of the hexagon.
.
....................
cm²
(1)
22. Shown below is isosceles triangle, ABC, where AB = BC
(a) Work out the size of angle BAC
.
.....................
°
(3)
(b) Work out the size of angle ABC
.
.....................
°
(1)
23. Humphrey is flying a kite.
The handle is held 80cm above the
ground. The kite is on a string which is
8m long.
The string makes an angle of 63° with the horizontal.
Calculate the height of the bottom of the kite above the ground.
.
.....................
m
(4)
24. A helicopter leaves Bristol and flies due east for
10 miles. Then the helicopter flies 8 miles north
before landing.
(a) Work out the direct distance of the helicopter from Bristol.
.
..............
miles
(3)
(b)Calculate the bearing of the helicopter from Bristol.
.
.....................
°
(3)
25. A boat is approaching a cliff with a lighthouse on top.
The cliff is 100m high and the lighthouse is 30m tall.
The angle of elevation from the boat to the top of the lighthouse is 20°
(a) Calculate the distance of the boat from the base of the cliff.
.
.....................
m
(3)
(b)Work out the angle of elevation from the boat to the top of the cliff.
.
.....................
°
(3)
26. ABCD is a trapezium
Angle BAD = 74°
CD = 19.2cm
AB =
26cm AM
= 2.5cm
Work out the size of angle ABC.
.
.....................
°
(5)
