April 4 th copyright2009merrydavidson CALCULATOR TODAY Happy Summer Birthdays to: Timmy Manley: 7/5...
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Transcript of April 4 th copyright2009merrydavidson CALCULATOR TODAY Happy Summer Birthdays to: Timmy Manley: 7/5...
April 4April 4thth
copyright2009merrydavidsoncopyright2009merrydavidson
April 4April 4thth
copyright2009merrydavidsoncopyright2009merrydavidson
CALCULATOR TODAY
Happy Summer Birthdays to:
Timmy Manley: 7/5th
Andrew Krasner: 8/14th
OBLIQUE TRIANGLES6.1 & 6.2
A triangle with NO right angles.
ANGLES/CAPITAL LETTERS
sides/small letters
A
B Ca
bclittle a is across from Big A
put calculator in
degree mode
SOLVE the triangleMeans to find the length of all sides and the measure of all angles.
To solve oblique triangles two pieces of information are needed and a TRIG FUNCTION.
Round sides to the nearest TENTH and angles to the nearest DEGREEunless otherwise
noted.
LAW OF SINES (you will use 2 of the 3 sections to make a proportion.
C
c
B
b
A
a
sinsinsin
Memorize this……..
This formula states that the ratio of any side of a triangle to the sine of the angle opposite that side is a constant (proportional) for a given triangle.
EX 1: Given triangle ABC with the measures shown below,
find b?
8
sin 57 sin 74
b57O 49O
AB
C
8
START with a chart.
Fill in what you know
Find angle C.
Solve the proportion
74
bsin74 = 8sin57
b = 8sin57 sin74
approx 7.0
a= b= c=
A= B= C=
a= b= c=8
A= 49 B=57 C=
EX 2: In triangle ABC if
A = 32, B = 57, and c = 14. Find angle C and
sides a and b.
a = b = c =
A = B = C =
7.4
11.7
91
a
b
C
You do this one. In a minute I will show you the answer.
EX 3: In triangle ABC, A = 1100, b = 7 and a =
9. Find angle B.a = b = c =
A = B = C =
47B
9 7
sin110 sin B
7sin110 = 9sinB
sinB = 7sin110 9
Use sine inverse1 7sin110
sin ( )9
B
EX 4: Given an oblique triangle with angle A = 490, and side
a = 8 and side b = 9, find angle B.
a = b = c =
A = B = C =
58B
You do this one. In a minute I will show you the answer.
EX 5: Find b
a = 10 b = c = 7
A = B = 51 C =
B C10
7 b
51O
A
a = b = c =
A = B = C =
You can not make a proportion
LAW OF COSINES is used when you can
not make a proportion.
6.2
a2 = b2 + c2 – 2bc cos A
b2 = a2 + c2 –2ac cos B
c2 = a2 + b2 – 2ab cos C
Memorize these……..
EX 5: Find b
B C10
7 b
51O
Aa = 10 b = c = 7
A = B = 51 C =
Using the law of cosines…..
b2 = a2 + c2 -2ac cos B
b2 = 102 + 72 -2(10)(7) cos 51
60.9b
EX 6: SOLVE the triangle.
A B7
5 4
C
a = 4 b = 5 c = 7
A = B = C =
Always find the “biggest” angle first! So find C.
“store” this to find the other parts.
c2 = a2 + b2 -2ab cos C72 = 42 + 52 -2(4)(4) cos
C49 = 41-2(4)(4) cos C
8 = -2(4)(4) cos C
1 8cos ( ) 104
32C
EX 6: SOLVE the triangle.
A B7
5 4
C
a = 4 b = 5 c = 7
A = B = C = 104
Now use Law of Sines
to find A or B. Then
use the sum of angles in
a triangle is 180o to
find the other angle.
44
32
B
A
EX 7: SOLVE the triangle.
B C6
8 b
60O
A
a = b = c =
A = B = C =
What should you find first???
little b
7.2bStore this!
Now find angle A or C.
46
74
A
C