1. Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012

2. Sine, Cosine and Tangent Ratios
Trigonometric Ratios
sin Ɵ = 𝐎 𝐇
cos Ɵ = 𝐀 𝐇
tan Ɵ = 𝐎 𝐀
SOH
CAH
TOA H O Ɵ A

3. Sine, Cosine and Tangent Ratios
SOHCAHTOA
hyp
opp
adj

4. Practice
Find the height of a tree which casts a shadow of 12.4 meters when the sun makes an angle of 52° to the horizon.
15.9 m

5. Sine, Cosine and Tangent Ratios
Solving for Angles:
Label the triangle with hyp, opp, adj,
Choose the correct ratio from SOHCAHTOA
Set up the equation
Solve by using the inverse.
MAKE SURE CALCULATOR IS IN DEGREES !!!

6. Find, to 1 decimal place, the measure of the angle marked  in:
Practice
Find, to 1 decimal place, the measure of the angle marked  in: θ
5.92
2.67 4 θ 7
29.7 °
63.2 °

7. Find, to 1 decimal place, the measure of the angle marked  in:
Practice
Find, to 1 decimal place, the measure of the angle marked  in:  θ 20 21 2 5
43.6 °
23.6 °

8. Find to 4 sig. figs the unknowns in the following diagrams:
Practice
Find to 4 sig. figs the unknowns in the following diagrams:
12.80
36.51 °

9. Practice
A chord of a circle subtends an angle of 112° at its center. Find the length of the chord if the radius of the circle is 6.5 cm
10.8 cm

10. Practice
A rhombus has diagonals of length 10cm and 6 cm respectively. Find the smaller angle of the rhombus.
61.9 °

11. Practice
Find x given:
12.2 cm

12. Practice
An A-frame house has the shape of an isosceles triangle with base angles of 70. The oblique walls of the building are 12 meters long. How wide is the building at ground level?
8.21 m

13. Practice
A builder designs a roof structure as illustrated. The pitch of the roof is the angle that the roof makes with the horizontal. Find the pitch of the roof.
30.5 °

14. Practice
A cube has sides of length 12 cm. Find the angle between the diagonal AB and one of the edges at B.
35.3 °

15. Find the angle that: a) PV makes with QV b) SU makes with SQ
Practice
Find the angle that: a) PV makes with QV b) SU makes with SQ

16. Find the angle between DG and the base plane EFGH.
Practice
Find the angle between DG and the base plane EFGH.

17. The base is 10m by 10m and its slant edges are 14 m long. Find:
Practice
The given figure shows a square-based pyramid with apex directly above the center of its base.
The base is 10m by 10m and its slant edges are 14 m long. Find:
The length of MC
The angle that NC makes with the base ABCD

18. Practice
A symmetric square-based pyramid has base lengths of 6 cm and a height of 8 cm as shown. Find the measure of: a) angle TNM b) angle TRM

19. Angles of Depression and Elevation
The angle of elevation is the angle you lift your
eyes through to look at something above.

20. Angles of Depression and Elevation
The angle of depression is the angle you lower your
eyes through to look at something below.

21. Practice
From a vertical cliff 80 meters above sea level, a fishing boat is observed at an angle of depression of 6°. How far out to sea is the boat?
761 m

22. Practice
Find the angle of elevation from a bench to the top of an 80 meter high building if the bench is 105 meters from the foot of the building.
IBID text, Studies, page 477, #4
37.3°

23. Practice 113.8 m The angle of depression from the roof of a building A
to the foot of a second building B across the same street
and 40 meters away is 65°. The angle of elevation of the
roof of building B to the roof of building A is 35°.
How tall is building B?
IBID text, SL, page 295
113.8 m

24. Practice
From a window, 29.6 meters above the ground, the angle of elevation of the top of a building is 42°, while the angle of depression to the foot of the building is 32°. Find the height of the building.
Ibid text, studies, page 477 #9
72.3 m

25. Practice
Ingrid measures the angle of elevation from a point on level ground to the top of a building 120 meters high to be 32°. She walks towards the building until the angle of elevation is 45°. How far does she walk?
H&H text, Studies, page 329, #8
72.0 m