Transcript Chapter 9: Pythagorean Theorem

8-3:
Trigonometry

Objectives
To use the sine, cosine, and tangent ratios to
determine side lengths and angle measures in
right triangles
Trigonometry Ratios
Trigonometry:
The study of the relationship between the sides and the
angles of a triangle
Sine of A
Opposite
sin A =
Hypotenuse
B
Opposite
Cosine of A
C
Tangent of A
A
Adjacent
SOHCAHTOA
Adjacent
cos A =
Hypotenuse
tan A =
Opposit e
Adjacent
SOHCAHTOA
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Calculators in
“degree”
mode!!
x
Examples
SOHCAHTOA
8 ft
500 ft
A
350 0
20
15 ft
sin 200 =
x (sin
200)
x=
500
sin 20 0
x=
500
x
= 500
500
0.342
x ≈ 1,462
872 ft
p. 510: 1-6,
11-19
tan A =
8
15
tan A = 0.5333
Using Inverses
> You know two sides
> You want to find the measure of
one of the acute angles.
8-3 DAY 2
SOHCAHTOA
S O H
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T O A
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SOHCAHTOA
x
8 ft
500 ft
A
200
15 ft
sin 200 =
x (sin
200)
x=
500
sin 20 0
x=
500
x
= 500
500
0.342
x ≈ 1,462 ft
tan A =
8
15
tan A = 0.5333
A = tan-1 0.5333
A ≈ 280
SOHCAHTOA
B
754 ft
500 ft
cos B =
500
754
B = cos-1 0.6631
B ≈ 480