Answer:
Option D. m<A = 43, m<B = 55, a = 20
Explanation:
1. Determination of angle B.
Angle C = 82
Opposite C (c) = 29
Opposite B (b) = 24
Angle B =?
Using Sine rule, we can obtain the value of angle B as follow:
b/Sine B= c/Sine C
24/Sine B = 29/Sine 82
Cross multiply
29 × Sine B = 24 × Sine 82
Divide both side by 29
Sine B = (24 × Sine 82) /29
Sine B = 0.8195
Take the inverse of Sine.
B = Sine¯¹ (0.8195)
B = 55
2. Determination of angle A.
Angle C = 82
Angle B = 55
Angle A =?
The value of angle A can be obtained as follow:
A + B + C = 180 (sum of angle in a triangle)
A + 55 + 82 = 180
A + 137 = 180
Collect like terms
A = 180 – 137
A = 43
3. Determination of side a (Opposite A)
Angle C = 82
Opposite C (c) = 29
Angle A = 43
Opposite A (a) =?
The value 'a' can be obtained as by using sine rule as illustrated below:
a/Sine A = c/Sine C
a/Sine 43 = 29/Sine 82
Cross multiply
a × Sine 82 = 29 × Sine 43
Divide both side by Sine 82
a = (29 × Sine 43) /Sine 82
a = 20
Therefore,
m<A = 43, m<B = 55, a = 20