The length of b and angle B and C are 3cm, 45 Â degrees and 79 degrees respectively.
To determine the angles and length of sides, we use the sine rule
The sine rule is thus:
[tex]\frac{sin A}{a}= \frac{sin B}{b} = \frac{sin C}{c}[/tex]
Given;
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
[tex]b = \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{sin B}{3}[/tex]
cross multiply
0. 682 × 3 = sin B × 2. 5
sin B = 0. 7065
[tex]B = sin ^-^1 (0. 7065)[/tex]
B = 45°
Hence, the length of b and angle B and C are 3cm, 45 Â degrees and 79 degrees respectively.
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