an archer stands 100 feet away from a target and aims for the bulls eye that rests 30 feet above the...
DESCRIPTION
Today’s Objective To use the Law of Sines to find measurements in triangles.TRANSCRIPT
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