Date : 2/7
Aim : To use trigonometric ratios for indirect measurements of right triangles.

• Derived from Greek words, “trigonon" which means triangle, and "metria” which means measure.
• Trigonon metria = “triangle measurement”
• Sine comes from the Latin word sinus meaning a curve or fold.
• Cosine was originally written " co.sine," short for
COMPLEMENTI SINUS : the sine of the complementary angle.
• Tangent comes from the Latin word tangens which is a straight line which touches a circle at one point.

 

 

Tangent of
  length length of leg Opposite
 of Adjacent


• SOH
• CAH
• TOA
Sin

Opposite
Hypotenuse
Cos

Adjacent
Hypotenuse
Tan

Opposite
Adjacent

Sin A
 a c
Cos A
 b c
Tan A
 a b
B
C a b c
A

•
Find the lengths of a and c .
A
Sin 7 3
 
29 c c

29
Sin 73
 c

30 .
3
Tan 7 3
 
29 a

8 .
9 a a

29
Tan 73

29 c
C
73
 a
B

y tan 32 o
= opp. adj.
tan 32 o
=
11 x x tan 32 o x
= 11
=
11 tan 32 o x
11
0.6249
x 17.6
Sin 32
 
11 y y

11
Sin 3 2
 y

20 .
8

• A 20-ft wire supporting a flagpole forms a 35 o angle with the flagpole. To the nearest foot, how high is the flagpole?
Cosine Ratio
Cos 35
  x
20 x

20 ( Cos

35

) x

16 ft
20
35
 x

You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26° . You need to find the height and length of the base of the ramp .
sin 26 o sin 26 o
=
=
14 sin 26 o x opp. hyp.
14
6.1 ft.
x
= x cos 26 o
= adj. hyp.
cos 26 o
= y
14
14 cos 26 o
= y
12.6 ft.
y

Date : 2/8
Aim : To use these ratios for indirect measurements of right triangles.
Do Now: Find h .

Find the height h of the lamppost to the nearest inch.
tan 70 o
= opp. adj.
tan 70 o
= h
40
40 tan 70 o
= h
109.9
h
ANSWER
The lamppost is about 110 inches tall.

• Mount Everest –
29, 029 feet

• The Burj Khalifa, Dubai – 2717 feet

• Angel, Salto – Venezuela - 3,212 feet

Clinometer

Angle of
Elevation
42 °
42 °
Angle of
Depression

• The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye (the line of sight).
• If the object is below the level of the observer, then the angle between the horizontal and the observer's line of sight is called the angle of depression .

θ – angle of interest
Which angle is the angle of elevation?
Which angle is the angle of depression ?
A - angle of elevation
B – angle of depression
B
θ
A

How tall is the Empire State Building?
Exact Answer:
1,250 feet tall
76.5
°
300 ft

Since Mount Everest is 29, 029 feet tall, how far was Ms. Psillos from the mountain, if her angle of elevation was 55 °?
20,326.3 feet

Ms. Psillos is looking up at the waterfall in Angel,
Salto – Venezuela, which is 3,212 feet tall, and has an angle of elevation of 82 °. She wants to know the distance that her line of sight makes to the top of the waterfall?
3,243.6 feet

•
Find m

R to the nearest degree.
Tangent Ratio
R
Tan

R

47
41
Tan

R

1 .
146
41
S
Tan

1
1 .
146
 m

R
R

49

47
T