Trigonometric Ratios

How do you use trig ratios?

M2 Unit 2: Day 4

EXAMPLE 3Using tangent

Example 1

Find value of x in the triangle.

tan 70o=

opp. adj. Write ratio for

tangent of 70o.

tan 70o x. =

40.Substitute.

40 ● tan 70o = xMultiply each side by 40.

109.9 xUse a calculator to simplify.

ANSWER

x is about 110 .

Remember…SOHCAHTOA

x

700

40

EXAMPLE 2

Find the value of x.

SOLUTION

Use the tangent of an acute angle to find a leg length.

tan 32o=

opp. adj.

Write ratio for tangent of 32o.

tan 32o 11 =x Substitute.

x tan 32o = 11Multiply each side by x.

x = 11

tan 32o

Divide each side by tan 32o

x 11 0.6249 Use a calculator to find tan 32o

X ≈ 17.6Simplify

Example 2

Remember…SOHCAHTOA

Example 3: Find the value of each variable. Round decimals to the nearest tenth.

sin 65 cos 658 8

8 sin 65 8 cos 65

7.3 3.4

t u

t u

t u

Remember…SOHCAHTOA

*Once you have 2 sides of a triangle, you can use the Pythagorean Theorem to find the missing third side.

6 6sin 37 tan 37

6 sin 37 6 cos 37

sin 37 sin 37 cos 37 cos 37 10.0 y 8.0

x y

x y

x

Example 4: Find the value of each variable. Round decimals to the nearest tenth.

Example 5: Find the value of each variable. Round decimals to the nearest tenth.

cos 2334

o s sin 2334

o t

Example 6: Find the area of the triangle. Round decimals to the nearest tenth.

We need to know the lengths of the sides!

It is a 45o45o90o triangle!

4

24 2

2 2 4 2

2 2 2

45o

2 2

2 2

2 2

2 2

12

A bh

12 2 2 2

2A

Area is 4 square centimeters!

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

x4

4 2a

12

A bh

112 4 3

2A

241.6 mA 224 3 mA

Example 8: Find the perimeter of the triangle. Round decimals to the nearest tenth.

We need to use a trig ratio. 6tan 22o

y

16.02 6 14.85P

36.9 feetP

14.85y

6sin 22o

x

16.02x

Example 9: Find the perimeter of the triangle. Write your answer in simplest radical form.It’s a 30o60o90o triangle.

6 12 6 3P

18 6 3 feetP

60o

12

6 3

Example 10: Find the perimeter of the triangle. Round decimals to the nearest tenth.

We need to use a trig ratio.

tan 209

o w

9 9.58 3.28P

91.9 in.P

3.28y

9cos 20o

v

20o

9.58v

Homework: pg 159-160 #11-19 oddspg 168 #9-12 all

MAKE SURE YOU SHOW YOUR WORK AND DRAW THE DIAGRAMS!