Date post: | 25-May-2015 |
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Demonstration TeachingIn
Trigonometry
Right Triangle
Acute Triangle
Obtuse Triangle
TriangleSolved
three sides
three angles
Right Triangle
B B B B
a
Acute TriangleObtuse Triangle
Oblique Triangles
Oblique Triangle
is a triangle which does not contain a right angle.
How then do we solve oblique
triangles?
The Law of SinesIn any triangle ABC, the sides are proportional to
the sines of the opposite angles.
= = or reciprocal form
= =
Case II: Given two angles and the included side between them (ASA)
Case I: Given two angles and a side opposite one of them (AAS)
Case III: Given two sides and an angle opposite one of them Case IV: Given two sides and the included angle between them
Case v: Given three sides
Case I. Given two angles and a side opposite to one of them. (AAS)
Given: A = 48° C = 102° c = 25cm
Unknown : B , a, c
A
C
B
a=? b =?
c= 25 cm
48°
102°
?
Case I. Given two angles and a side opposite to one of them. (AAS)
Given: A = 63° C = 79° a= 12 in
Unknown : B , b, c
In ABC, A = 63°, B = 79°, and a = 12 in. Find ▲the length s of the other two sides and the measure of the third angle, C.
BA
C
a =12 inb =?
c= ?
63°
79°
?
Given: A = 75° C = 85° b = 10 cm
Unknown : B , a, c
Case II. Given two angles and the included side between them. (ASA)
A Bc = ?
b=10 cm a =?
C
85°
75° ?
Given: A = 59° C = 49° b = 13 cm
Unknown : B , a, c
Case II. Given two angles and the included side between them. (ASA)
A Bc = ?
b=13 cm a =?
C
59°
49°
?
is a triangle which does not contain a right angle.
Oblique Triangle
Law of SinesIn any triangle ABC, the sides are proportional to the
sines of the opposite angles. = = or reciprocal form
= =
Case I: Given two angles and a side opposite one of them (AAS)
Case II: Given two angles and the included side between them
(ASA)
Case III: Given two sides and an angle opposite one of
them
Assignment:
Answer Exercises 6.2 p. 167.