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!