Answer: To solve for side
a using the Law of Sines, we'll use the formula:
sin
=
sin
=
sin
sinA
a
=
sinB
b
=
sinC
c
Given
=
132
°
A=132°,
=
28
°
C=28°, and
=
10
b=10, we can plug in these values and solve for
a:
sin
132
°
=
10
sin
sin132°
a
=
sinB
10
First, we need to find
B using the fact that the sum of angles in a triangle is
180
°
180°:
=
180
°
−
−
=
180
°
−
132
°
−
28
°
=
20
°
B=180°−A−C=180°−132°−28°=20°
Now, we can plug in
=
20
°
B=20° and solve for
a:
sin
132
°
=
10
sin
20
°
sin132°
a
=
sin20°
10
Rearranging to solve for
a:
=
10
×
sin
132
°
sin
20
°
a=10×
sin20°
sin132°
Now, we can calculate
a:
≈
10
×
sin
132
°
sin
20
°
≈
10
×
0.866
0.342
≈
10
×
2.535
=
25.35
a≈10×
sin20°
sin132°
≈10×
0.342
0.866
≈10×2.535=25.35
So, the length of side
a is approximately
25.35
25.35 (rounded to the nearest hundredth).