SECTION 8-6SECTION 8-6Law of SinesLaw of Sines

Jim Smith JCHSJim Smith JCHS

3108.4.493108.4.49Use the Law of Sines to find missing side lengths and/or Use the Law of Sines to find missing side lengths and/or angle measures in non-right trianglesangle measures in non-right triangles

A Car Runs Into A Telephone A Car Runs Into A Telephone Pole AndPole And

Knocks It Off Perpendicular To Knocks It Off Perpendicular To The Ground By 9°. If The PoleThe Ground By 9°. If The Pole’’s s

ShadowShadowIs 57 Feet Long And The Angle Is 57 Feet Long And The Angle

Of Of Elevation From The Ground To Elevation From The Ground To

The Top The Top Of The Pole Is 48°, How Can We Of The Pole Is 48°, How Can We

Find Find The Height Of The Pole?The Height Of The Pole?

Let a = 7 cm, ∠B = 45°, and ∠C = 75°.

Is there a unique triangle with the given angle and side measures? Why?    How might you determine the measures of the missing angle and sides?

What method did we use to findthe height of a tree?

What measures did we need tofind the height of a tree or a pole?

If the pole is leaning at an angle,why can’t we use sin, cos, or tangent?

The Law Of Sines Allows Us To WorkThe Law Of Sines Allows Us To Work

With Triangles Other Than RightWith Triangles Other Than Right

Triangles. Triangles.

In A Triangle, The Ratio In A Triangle, The Ratio

Of The Sine Of An Angle And Of The Sine Of An Angle And

The Length Of The Side The Length Of The Side

OppositeOpposite

That Angle Are The Same That Angle Are The Same

For For

Each Pair Of Angles And Each Pair Of Angles And

Sides.Sides.

They are ___________________They are ___________________

Proportional

AA

BB

CC

cc aa

bb

c

C

b

B

a

A sinsinsin

Students will be able to writethe law of Sines formula

Students will be ableStudents will be ableto find the missing side ofto find the missing side ofa non-right trianglea non-right triangle

AA

BB CC

85°85°

70°70°

XX

1515

X

70sin

15

85sin

)70(sin15)(85sin X

85sin

)70(sin15

85sin

)(85sin

X

85sin

)70(sin15X

15.14X

AAS

ACT FORM

X

70sin

15

85sin

)70(sin15)(85sin X

85sin

)70(sin15

85sin

)(85sin

X

85sin

)70(sin15X

15.14X

X

9396.

15

9961.

)9396(.159961. X

9961.

10.14

9961.

9961.

X

15.14X

“Another way to skin a cat”

Back To The Car AndBack To The Car And Telephone PoleTelephone Pole

A Car Runs Into A Telephone A Car Runs Into A Telephone Pole AndPole And

Knocks It Off Perpendicular To Knocks It Off Perpendicular To The Ground By 9°. If The PoleThe Ground By 9°. If The Pole’’s s

ShadowShadowIs 57 Feet Long And The Angle Is 57 Feet Long And The Angle

Of Of Elevation From The Ground To Elevation From The Ground To

The Top The Top Of The Pole Is 48°, How Can We Of The Pole Is 48°, How Can We

Find Find The Height Of The Pole?The Height Of The Pole?

9°9°

575748°48°

Do you know how to solve it now?Do you know how to solve it now?

9°9°

48°48°5757AA

BB

CC

xx

990 BCA

81°81°

51°51°

57

51sin48sin

x

48sin57)(51sin x

51sin

48sin57x

51.54x

LetLet’’s find an angle…s find an angle…Look at a right triangle fromLook at a right triangle from

last week first …last week first …

10102222

22

10 xofsin

00.27x

xx

55 33

xx 50°50°

5

50sin

3

sinx

)50(sin3)(sin5 x

5

)50(sin3sin x

36.27x

Students will be ableStudents will be ableto find the missing angle ofto find the missing angle ofa non-right trianglea non-right triangle

Add This

xx1717

92°92°1414

17

92sin

14

sinx

17

9993.

14

sinx

99.13)(sin17 x

17

99.13sin x

)71(13.99sin 2 nd

38.55x

SSA SSA be be carefulcareful

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