Transcript IB Studies Topic 5.2bx

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, 2004
AND
Mathematical Studies Standard Level
Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman
Oxford University Press, 2012
Sine, Cosine and Tangent Ratios
Trigonometric Ratios
sin Ɵ =
𝐎
𝐇
cos Ɵ =
SOH
CAH
H
O
Ɵ
A
𝐀
𝐇
tan Ɵ =
TOA
𝐎
𝐀
Sine, Cosine and Tangent Ratios
SOHCAHTOA
Opp
Sin 
Hyp
hyp
opp
Adj
Cos 
Hyp
Opp
Tan 
Adj

adj
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
Sine, Cosine and Tangent Ratios
Solving for Angles:
1.
2.
3.
4.
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 !!!
Practice
Find, to 1 decimal place, the measure of the angle marked  in:
4
2.67
5.92
θ
θ
7
29.7 °
63.2 °
Practice
Find, to 1 decimal place, the measure of the angle marked  in:

20
2
5
θ
21
43.6 °
23.6 °
Practice
Find to 4 sig. figs the unknowns in the following diagrams:
12.80
36.51 °
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
Practice
A rhombus has diagonals of length 10cm and 6 cm
respectively. Find the smaller angle of the rhombus.
61.9 °
Practice
Find x given:
12.2 cm
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
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 °
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 °
Practice
Find the angle that:
a) PV makes with QV
b) SU makes with SQ
Practice
Find the angle between DG and the base plane EFGH.
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:
a) The length of MC
b) The angle that NC makes
with the base ABCD
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
Angles of Depression and Elevation
The angle of elevation is the angle you lift your
eyes through to look at something above.
Angles of Depression and Elevation
The angle of depression is the angle you lower your
eyes through to look at something below.
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
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.
37.3°
Practice
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?
113.8 m
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.
72.3 m
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?
72.0 m