right triangle trigonometry three basic trig ratios: sin θ = opposite/hypotenuse cos θ =...
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Right Triangle Trigonometry
Three Basic Trig Ratios:
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
Adjacent Side
Hypotenuse
Opp
osite
sid
e
Find the sine, cosine and tangent of angle A. Round your answers to the nearest ten thousandth.
A9 cm
4.5 cm10.1 cm
sin A =
cos A =
tan A =
4.5 / 10.1 ≈ 0.4455
9 / 10.1 ≈ 0.8911
4.5 / 9 ≈ 0.5000
Use a calculator to find the value of each trigonometric ratio to the nearest
ten thousandth. Make sure your calculator is in degree mode.
1. sin 45° ≈
2. cos 47° ≈
3. tan 48° ≈
0.7071
0.6820
1.1106
Use a calculator to find the measure of each angle to the nearest degree. *Remember to
use the 2nd button prior to typing the trig button.
1. sin A = 0.7547
2. tan A = 2.3456
3. cos B = 0.6947
4. sin A = 0.6589
5. tan C = 1.9832
6. cos B = 0.0136
1. A ≈ 49°
2. A ≈ 67°
3. B ≈ 46°
4. A ≈ 41°
5. C ≈ 63°
6. B ≈ 89°
Solve the triangle for all sides and angles. Round the sides to the nearest tenth and
angles to nearest degree.
A
B
C
a = 30
b = 20
A = a =
B = b =
C = c =
Mark what you are given30
20
90°
c =
To find c, use Pythagorean Theorem: 302 + 202 = c2
36.1
Next find A:tan A = 30/20
56°
34°
Last find B:180° – 90° – 56° =
Solve the triangle for all sides and angles. Round the sides to the nearest tenth and
angles to nearest degree.
A
B
C
a =
b =
A = a =
B = b =
C = c =
Mark what you are given53°
90° 50
c = 50
Find B:180° – 90° – 53° =Next find a:sin 53° = a / 50
Last find b:cos 53° = b / 50
53°
37°
39.9
30.1
Solve the triangle for all sides and angles. Round the sides to the nearest tenth and
angles to nearest degree.
A
B
C
a = 15
b =
A = a =
B = b =
C = c =
Mark what you are given56° 15
90°
c =
Find B:180° – 90° – 56° =Next find b:tan 56° = 15 / bso, b = 15 / tan 56°
Last find c:sin 56° = 15 / cso c = 15 / sin 56°
56°
34°
18.1
10.1
Reciprocal Functions
Three Basic Trig Functions:
sin θ
cos θ
tan θ
Three Reciprocal Trig Functions:
csc θ = hypotenuse/opposite
sec θ = hypotenuse/adjacent
cot θ = adjacent/opposite
β
3
4
Find all six trigonometric functions for angle β.