SEC. 8 – 3 THE TANGENT RATIO

Objectives/DFA/HW

Objective: SWBAT use the tangent ratios to determine side lengths in triangles.

DFA: p.434 #6bjecti

HW: pp.434-437 (2-28 even, 48-64 even)s pp.434-436 (2-28 even, 48-58 even)

This only for right Δs!!• Trigonometry

• Greek Word• Trigon → Triangle• Metron → Measure

• Trigonometry Ratio – Ratio of the lengths of sides of a right Δ.

• The tangent is just a button on your calculator!

TaTann** Make sure you calculator is in

Degrees!!

Tangent Ratio

• Tangent Ratio – Ratio of the length of the opposite leg from an to the length of the leg adjacent to the same .

A

C B

b

a

c

* Can’t use the right , C

Tangent A =

Length of leg Opposite of ALength of leg Adjacent of A

Tangent A =

ab

Writing tangent ratios• Write the tangent ratio of T and U.

T

U

S

6

8

10

Tangent =OppositeAdjacent

Tangent T = 8

6TSUS

= Tangent U =

TSUS 6

8=

** Tangent ratio for T & U are reciprocals

You can use the tangent ratio to find the measure of a distance that is difficult to measure directly.

• Example 1: Find w.

10

w

54

Step 1: Set up the Tangent RatioTan 54 =opp

adj

Tan 54 =w10

1.376 =w10

13.76 = w

Ex. 2: Solve for the variable using the tangent ratio.

70°

8cm

x

Step 1: Set up the tangent ratio.

Tan 70 =oppadj

Tan 70 =8x

2.747 = 8x Multiply both sides

by the denominator, x2.747x = 8

x = 2.9

The Tangent Inverse: Tan-1

• Just another button on your Calculator!• Use it when you have the two sides of a Δ and are trying

to find a missing .

TanTanTan-1Use the SHIFT

(2nd) Key to get to it.

Once you press it, it should look like this:Tan-1 (

Ex.3: Using the Tan-1

• Use the Tan-1 to solve for the missing .

12mm

5mm

y°

Step 1: Set up the Tan Ratio

Tan y = oppadj

Tan y =512

Tan y = .4167

At this point you will use the Tan-1:

1)Hit shift Tan to get to

Tan-1(

2) Type in the decimal and hit enter

Tan-1 (.4167) =

22.6°

Ex.4: Solve for mZ

8mil8mileses

6

6

mil

es

mil

es

x Y

ZTan Z = opp

adj

Tan Z = 86

Tan Z = 1.333

Tan-1 (1.333) = mZ

mZ = 53.1°

What have I learned???

• Tan =

• Use Tan-1 when looking for an measure.

Opposite SideAdjacent Side