The length of b and angle B and C are 3cm, 45 degrees and 79 degrees respectively.
How to determine the parameters
To determine the angles and length of sides, we use the sine rule
Given;
a = 2. 5cm
c = 3. 6cm
∠A = 43°
Let's find angle C
[tex]\frac{sin 43}{2. 5} =\frac{sin C}{3. 6}[/tex]
cross multiply
0. 682 × 3. 6 = sin C × 2. 5
sin C = 2. 4552/ 2. 5
C = [tex]sin^-^1 ( 0. 982)[/tex]
C = 79°
To find length of b
[tex]b = \sqrt{c^2 - a^2}[/tex]
substitute the values
b = [tex]\sqrt{3. 6^2 - 2. 5^2}[/tex]
b = 2. 59 cm
b = 3cm
To find angle B, we have
[tex]\frac{sin 43}{2. 5} = \frac{sinB}{3}[/tex]
cross multiply
0. 682 × 3= sin B × 2. 5
sin B = 0. 7065
B = [tex]sin^-^1(0. 7065)[/tex]
B = 45°
Hence, the length of b and angle B and C are 3cm, 45 degrees and 79 degrees respectively.
Learn more about sine rule here:
https://brainly.com/question/12827625
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