Chapter 9 Non-right angled triangle trigonometry

Chapter 9Non-right angled triangle trigonometry
MariaWinquest& SamZakalowski
A – Areas of Triangles
Area = ½ base x heightA = ½absinC
A
B
C
X cm
17 cm
68 °
150 = ½ (17) (x) (sin 68)150 = 8.5 (x) (sin 68)150/8.5 = (x) (sin 68)17.65/sin 68 = x19.01 = x
If triangle ABC has area 150 cm2find the value of x:
B- The Cosine Rule
The cosine rule can be used to solve triangles given :Two sides and an included angleThree sidesc2=a2+b2–2abcosCTo find the angles if we know all the sides we can use these formulas:cosA =cosB =cosC =
X cm
8 cm
11 cm
70 °
112= 82+ x2-2(x) (8)cos70121 = 64 + x2-16xcos700 = - 57 + x2-16xcos700= -57 + x2– 5.47xX2-5.47x – 57
10.76
-5.29
Find x:
The Quadratic Formula:
The Ambiguous CaseThis case only occurs when you use the Sine rule.An example of this case would be:Find the measurement of angle C in the triangle ABC in AC= 7cm, AB= 11cm, and angle B measures 25°
A
C
C
B
25°
7cm
7cm
11cm
Cross multiply
Divide by 7
Sin-1
C 41.61 ORC 138.39
C – The Sine Rule
9C.1 1b) Find the value ofx:
Use thesine rulewhen given:One side and two anglesTwo sides and a non-includedangle
11 cm
115°
48°
xcm
xsin48=11sin115
x=
x= 13.415 cm
c
b
a
A
B
C
D – Using the Sine and Cosine Rules
Review :Use thecosine rulewhen given:three sides two sidesan included angleUse thesine rulewhen given:One side and two anglesTwo sides and a non-included angle, but beware of theambiguous casewhich can occur when the smaller of the two given sides is opposite the given angle.