1. Right-angled Trigonometry

2. Right-angled Trigonometry
Opposite A

3. Right-angled Trigonometry
Hypotenuse
Opposite A

4. Right-angled Trigonometry
Hypotenuse
Opposite A
Adjacent

5. Right-angled Trigonometry
Opp
Hyp A
Adj

6. Right-angled Trigonometry
Opp
Hyp A
Adj

7. Right-angled Trigonometry
Opp
Hyp A
Adj

8. Right-angled Trigonometry
Opp
Hyp A
Adj
The Old Arab

9. Right-angled Trigonometry
Opp
Hyp A
Adj
The Old Arab Sat On His

10. Right-angled Trigonometry
Opp
Hyp A
Adj
The Old Arab Sat On His Camel And Hiccupped

11. Calculate the length of PQ in the triangle PQR
Example
Calculate the length of PQ in the triangle PQR P R
52 cm
32 Q

12. Calculate the length XY in the triangle XYZ
Example
Calculate the length XY in the triangle XYZ X Y
59
4.6 cm Z

13. Calculate the length of BC in the triangle ABC.
Example
Calculate the length of BC in the triangle ABC. B
5 cm
24 A C

14. Example
A surveyor, P, is 1000m away on horizontal ground from the foot of a radio mast, QR. From P the angle of elevation of the top, R, of the mast is 20. Find the height of the mast. Assume the surveyor’s height to be negligible.

15. Example
From the top of a vertical cliff 100m high the angle of depression of a boat out at sea is 32. How far is the boat from the foot of the cliff?

16. Example Calculate the size of angle A in the triangle ABC
4 cm A C
6 cm

17. Find the size of angle x in each of the following (i)
Example
Find the size of angle x in each of the following
(i)
1.2 cm x
4.7 cm

18. 10 cm
3.7 cm x
(ii)

19. 7 cm
12 cm x
(iii)

20. Calculate the size of angle PQR in the triangle below.
Example
Calculate the size of angle PQR in the triangle below.
8 cm
6 cm P R

21. Example
The road from village A runs due West for 5 miles to a fort B. A television mast is due South of B and 4 miles from B. Find the distance and bearing of the mast from A.

22. Example
The figure is a pyramid on a square base ABCD. The edges of the base are 30cm long and the height, EH, of the pyramid is 42cm. Find
a) the length of AC
b) the angle EAH E C D B A H

23. (iii) the total surface area of the prism.
Example
ABCDEF is a prism with a triangular cross-section. , BC = 8m, AB = 6m and CD = 20m.
Find
(i) AC (ii) BD
(iii) the total surface area of the prism. A F E C B D