Transcript Basic Right triangle trig

Right Triangle Trigonometry
Three Basic Trig Ratios:
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
Opposite side
sin θ = opposite/hypotenuse
Adjacent Side
Find the sine, cosine and tangent of
angle A. Round your answers to the
nearest ten thousandth.
4.5 cm
sin A =
10.1 cm
4.5 / 10.1 ≈ 0.4455
cos A = 9 / 10.1 ≈ 0.8911
tan A = 4.5 / 9 ≈ 0.5000
9 cm
A
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° ≈ 0.7071
2. cos 47° ≈ 0.6820
3. tan 48° ≈ 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
1. A ≈ 49°
2. tan A = 2.3456
2. A ≈ 67°
3. cos B = 0.6947
3. B ≈ 46°
4. sin A = 0.6589
4. A ≈ 41°
5. tan C = 1.9832
5. C ≈ 63°
6. cos B = 0.0136
6. B ≈ 89°
Solve the triangle for all sides and angles.
Round the sides to the nearest tenth and
angles to nearest degree.
Mark what you are given
A = 56°
a = 30
B = 34°
b = 20
C = 90°
c = 36.1
B
c=
a = 30
C
b = 20
To find c, use Pythagorean
Theorem: 302 + 202 = c2
Next find A:
Last find B:
tan A = 30/20
180° – 90° – 56° =
A
Solve the triangle for all sides and angles.
Round the sides to the nearest tenth and
angles to nearest degree.
Mark what you are given
A = 53° a = 39.9
B = 37°
C = 90°
b = 30.1
c = 50
Find B:
180° – 90° – 53° =
Next find a:
sin 53° = a / 50
B
a=
c = 50
53°
C
Last find b:
cos 53° = b / 50
b=
A
Solve the triangle for all sides and angles.
Round the sides to the nearest tenth and
angles to nearest degree.
Mark what you are given
A = 56° a = 15
B = 34°
b = 10.1
C = 90°
c = 18.1
Find B:
180° – 90° – 56° =
Next find b:
tan 56° = 15 / b
so, b = 15 / tan 56°
B
c=
a = 15
56°
C
b=
Last find c:
sin 56° = 15 / c
so c = 15 / sin 56°
A
Reciprocal Functions
Three Basic Trig Functions: Three Reciprocal Trig Functions:
sin θ
csc θ = hypotenuse/opposite
cos θ
sec θ = hypotenuse/adjacent
tan θ
cot θ = adjacent/opposite
Find all six trigonometric
functions for angle β.
β
3
4