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171 The Trigonometric Ratios

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Fill in the missing lengths for the special right triangle, and then find the ... We first set up a survey post directly across the river from some landmark (like ... – PowerPoint PPT presentation

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Title: 171 The Trigonometric Ratios


1
17-1 The Trigonometric Ratios
Purpose Learn 3 trig ratios (Sin, Cos, or Tan)
for right triangles, so that later on you can
find the missing side, or angle of a right
triangle.
2
Trigonometry The study of the measurement of
triangles
B
c
a
A
C
b
3
Sin ltA
Opposite Leg
Hypotenuse
B
c
a
A
C
b
4
Cos ltA
Adjacent Leg
Hypotenuse
B
c
a
A
C
b
5
Tan ltA
Opposite Leg
Adjacent Leg
Tan your legs, opp on top
B
c
a
A
C
b
6
SOHCAHTOA
B
Opposite Leg
Hypotenuse
c
a
A
C
Adjacent Leg
b
7
Find the sin, cos,and tan of angle A
B
13
5
A
C
12
8
Fill in the missing lengths for the special right
triangle, and then find the sin, cos, and tan of
a 30º,60º, 45º
30
45
1
45
60
1
9
  • Pg. 559
  • (2acefj,3bdfk,
  • 5-8,10,12,18,19)

10
  • Surveying the Uses of Trigonometry
  • Some people just do not know how to have fun.
    They think everything has to be useful. Luckily,
    the sine, cosine, and tangent functions do have a
    lot of real-world uses.
  • Surveyors use the tangent function a lot. For
    example, they can use trigonometry to figure out
    the distance across rivers.
  • We first set up a survey post directly across the
    river from some landmark (like a tree). Then we
    head downstream a distance that we can measure
    in this case, 400 meters. Thats the red
    horizontal line in the drawing.
  • Now we take a sighting on the tree from
    downstream. Thats the black line in the drawing.
    The surveying instruments will tell us what our
    sighting angle is. In this case, its 31 degrees.
  • We know from the previous page that the tangent
    of 31 degrees is equal to the length of the blue
    line divided by the length of the red line (400
    meters). So, if we multiply the tangent of 31
    degrees by 400 meters, well get the distance
    across the river.
  • The tangent of 31 degrees is about 0.60. That
    means that the distance across the river is 0.6
    times 400 meters, or 240 meters.
  • Real world alert! Wouldnt it have been simpler
    to just tie a rope to the tree, climb into a
    boat, go across the river, and measure how much
    rope you trailed out? In this case, it actually
    might be a good idea to physically cross the
    river to check the answer from our math. This
    gives us confidence that trigonometry really
    works.
  • After all, sometimes the real world gives us a
    river that is too difficult to cross or a cliff
    too dangerous to climb. In these cases the
    physical approach isnt possible. We need
    trigonometry--a mathematical technique we can
    trust for the answers we need.

11
(No Transcript)
12
6v3
  • Sin ltL ____
  • 12
  • 2.( )ltC 6
  • 6v3
  • 3. What are the measures of ltC and ltL
  • 4. Find the cosltA
  • 5. Find the sin ltK
  • 6. Simplify this expression by evaluating it
  • tan 45º
  • Cos 60

T
C
6
12
L
13
13
A
K
10
13
17.2 Numerical Trigonometry
  • Purpose
  • Use Sin, Cos, or tan to find measurements of a
    missing side of a right triangle, or an acute
    angle of a right triangle given two of the sides

14
Trig table on page 567
  • Use your table and your calculator to find these
    values
  • 1. sin 35º
  • 2. cos 57º
  • 3. tan 25º
  • Find ltA for each
  • 4. sinltA .45
  • 5. cos ltA .26
  • 6. Tan ltA 5

15
Find X
15
x
22º
16
Find X
20
32º
x
17
Find X
13
17º
x
18
H
65º
100 ft
19
Find X
13
17º
x
20
  • Pg. 564
  • (1a-e,2acegi,
  • 3-6,8,11,15-17,19)
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