Transcript Trigonometric Ratios How do you use trig ratios?
Trigonometric Ratios How do you use trig ratios?
M2 Unit 2: Day 4
Using tangent EXAMPLE 3
Remember…
SOHCAHTOA
Example 1 Find value of x in the triangle.
tan 70 o = opp. adj.
Write ratio for tangent of
70 o .
tan 70 o = x. 40.
Substitute.
x 40 ● tan 70 o 109.9
= x
x
ANSWER Multiply each side by
40
.
Use a calculator to simplify.
x is about
110
.
40 70 0
EXAMPLE 2 Example 2
Remember…
SOHCAHTOA
Find the value of x.
SOLUTION Use the tangent of an acute angle to find a leg length.
tan 32 o = opp. adj.
Write ratio for tangent of
32 o .
tan 32 o = 11
x
Substitute.
x tan 32 o = 11 x = 11 tan 32 o
Multiply each side by
x
.
Divide each side by tan
32 o
x
11 0.6249
Use a calculator to find tan
32 o
X ≈ 17.6
Simplify
Remember…
SOHCAHTOA
Example 3: Find the value of each variable. Round decimals to the nearest tenth.
t
sin 65
t
cos 65 8
u u
8
t
7.3
u
3.4
*Once you have 2 sides of a triangle, you can use the Pythagorean Theorem to find the missing third side.
Example 4: Find the value of each variable. Round decimals to the nearest tenth.
sin 37 6
x
tan 37 6
y
6 sin 37
x
x
sin 37 6 sin 37 cos 37 10.0 y
y
8.0
cos 37 cos 37
Example 5: Find the value of each variable. Round decimals to the nearest tenth.
cos 23
o
s
34 sin 23
o
t
34
Example 6: Find the area of the triangle. Round decimals to the nearest tenth.
2 2 We need to know the lengths of the sides!
It is a 45 o 45 o 90 o triangle!
2 2 45 o 4 2 4 2 2 2 4 2 2 2 2
A
1 2
bh A
1 2 2 2 Area is 4 square centimeters!
2 2
Example 7: Find the area of the triangle. Write your answer in simplest radical form and find the decimal approximation to the nearest tenth.
We need to know the altitude.
a
a
4 2
x4
A
1 2
bh A
1 2
A
24 3 m 2
A
41.6 m 2
Example 8: Find the perimeter of the triangle. Round decimals to the nearest tenth.
We need to use a trig ratio.
tan 22
o
6
y y
14.85
P
P
36.9 feet sin 22
o
6
x x
16.02
Example 9: Find the perimeter of the triangle. Write your answer in simplest radical form.
It’s a 30 o 60 o 90 o triangle.
12 60 o
6 3
P P
Example 10: Find the perimeter of the triangle. Round decimals to the nearest tenth.
We need to use a trig ratio.
20 o tan 20
o y
w
9 3.28
P P
91.9 in.
cos 20
o
9
v v
9.58
Homework: pg 159-160 #11-19 odds pg 168 #9-12 all MAKE SURE YOU SHOW YOUR WORK AND DRAW THE DIAGRAMS!