Answer:
A=73°, b=8.35 Units, c=9.4 Units
Step-by-step explanation:
To solve a triangle completely means to find all its sides and angles.
First, we determine Angle A.
53°+64°+A=180° (Sum of Angles in a Triangle)
107°+ A=180°
A=180°-107° =73°
Next, we determine the lengths of AC and AB.
Using Sine Rule
[TeX]\frac{a}{Sin A}= \frac{b}{Sin B}[/TeX]
[TeX]\frac{10}{Sin 73}= \frac{b}{Sin 53 }[/TeX]
Criss multiplying
b X sin73 = 10 X Sin 53
[TeX]b= \frac{10 X Sin 53}{Sin 73 }[/TeX]
b=8.35 Units
Similarly, for c
[TeX]\frac{a}{Sin A}= \frac{c}{Sin C}[/TeX]
[TeX]\frac{10}{Sin 73}= \frac{c}{Sin 64 }[/TeX]
Criss multiplying
c X sin73 = 10 X Sin 64
[TeX]b= \frac{10 X Sin 64}{Sin 73 }[/TeX]
c=9.4 Units
