An archer stands 100 feet away from a target and aims for the bull’s eye that rests 30 feet above the archer’s eye level.

How far does the arrow have to travel from the archer’s box to the bull’s eye?What angle of elevation does the archer need to use to hit the target?

Right TrianglesDay 11 – Law of Sines

Today’s ObjectiveTo use the Law of Sines to find

measurements in triangles.

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Homework: Worksheet – Using Law of Sines

Trigonometry in Non-Right Triangles

A

B

C

a

b

c

There are no right angles in ΔABC Draw an altitude from B

hhc

sin A sinC ha

Solve for hsin1A h

c

sinc A h

sin1C h

a

sina C hSet equations equal to each other sin sinc A a CDivide both sides by ac

sin sinc A a Cac ac

Simplifysin Aa

sinCc

Trigonometry

for all t

ypes

of triangles!

Law of Sines Law of Sines can be used to find the missing parts of triangles that are not

right.

A

B

C

a

b

c

Angles: A, B, C Sides: a, b, c *Notice the corresponding sides & angles

sin sin sinBb

Cc

Aa

OR

sin sin sinbBA

cC

a

**Law of Sines is also called:• Sine Formula• Sine Law• Sine Rule

Solve for x.

14

16

80o

x

sin sin sinBb

Cc

Aa

8016sin s

4in1x

801 1si n4 n 6 si x1616

8016si14 n

sin x

0.8617 sin x1sin 0.8617x

59.5x

A

a

B

b

Solve for x.

20

50o

x

sin sin sinBb

Cc

Aa

8520sin s 0in 5

x

85 20sin s 50inx sin85sin85

5sin20850

sinx

85o

15.32090.9962

x

15.4x

Solve the Triangle(Find all of the angles and sides)Figure not drawn to scale

X

Y

Z

98o

20

14

ANGLES

sin 9820

sin14Y

Which side/angle combo do we have to use?

20 sin 14 sin 98Y

14 sin98sin

20Y

sin 0.6932Y 1sin 0.6932Y 44Y

98 44 180m x 38m x

Solve the Triangle(Find all of the angles and sides)Figure not drawn to scale

X

Y

Z

98o

20

14

SIDESsin 9820

sin38x

Which side/angle combo do we have to use?

20 sin38 sin98x

20 sin38sin98

x

12.31320.9903

x

12.4x

44o

38o

Solving the following: A pilot is flying over a straight highway. He determined the angles

of depression between himself and mileposts A and be to be 32o and 48o. The mileposts are 5 mi apart.

Find the distance from the plane to mile marker A. What other angle measures can be found? What are we trying to find? How can we solve for x?

32o 48o

5 miA B

100o

48o

x

sin 48 sin1005x

5 sin 48sin100

x

3.77x mi

32o

Solving the following: A pilot is flying over a straight highway. He determined the angles

of depression between himself and mileposts A and be to be 32o and 48o. The mileposts are 5 mi apart.

Find the elevation of the plane. What are we trying to find? How can we solve for x?

32o 48o

5 miA B

100o

48o

3.77 mi

sin 323.77x

3.77 sin 32x

2.0x mi

32o

x

Did you meet today’s objective? When is it appropriate to use Law of Sines?

sin sin sinBb

Cc

Aa