Download 7.5 and 7.6 apply the tangent, sine and cosine ratios

7.5 and 7.6
apply the tangent, sine and cosine ratios
Trigonometry is the study of the measurement of triangles and of trigonometric functions and their applications.
A trigonometric ratio is a ratio of the lengths of two sides in a right triangle. Trigonometric ratios can be used to find the measure of a side or an acute angle in a right triangle.
You can write sine, cosine, and tangent ratios ONLY for the acute angles­­not for the right angle.
There are three basic trigonometric ratios: • sine
• cosine
• tangent
S
o
h
C
a
h
T
o
a
sin =
opposite leg
hypotenuse
cos =
adjacent leg
hypotenuse
tan =
opposite leg
adjacent leg
CAH
SOH
sin A = TOA
opposite
hypotenuse
cos A = tan A = adjacent
hypotenuse
opposite
adjacent
=
=
=
When using a calculator to find a trigonometric ratio, it must be in DEGREE mode. (press) 5 2 1 Choose: Degree
"Make Default"
Do not use a rounded answer to get another answer!
1. Use the picture to answer the following:
Name the . . . AC
CB
leg opposite A. __________ ∠
CB
leg adjacent to B. __________
∠
AC
leg opposite B. __________ ∠
AB
hypotenuse. __________
leg adjacent to A. __________
∠
2. Write the ratio for each of these trig functions.
Round decimals to hundredths (2 places).
Trig Function
Ratio
Decimal
sin A
4
5
cos A
3
5
4
3
3
5
4
5
3
4
.80
.60
1.33
.60
.80
.75
tan A
sin B
cos B
tan B
The sine of one acute angle will be equal to the cosine of the other acute angle.
The tangents of the two acute angles will be reciprocals.
4. Write an equation to find the value of each variable.
Solve. Round to hundredths.
7.25 = t
3.38 = u
5. Find the value of each variable. Round to hundredths.
a = 16.58
b = 27.55
6. Find the value of each variable. Round to hundredths.
15.92 = g
h = 18.78
7. Find the area and perimeter of the triangle. Round to the nearest tenth.
Find x:
15 = x
Find perimeter:
P = 67.3 ft
Find hypotenuse:
hyp = √801 Find area:
A = 180 ft2
homework
worksheet