The length of b and angle B and C are 2. 9cm, 44. 9 degrees and 79. 11 degrees respectively.
How to determine the parameters
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;
- a = 2. 5cm
- c = 3. 6cm
- ∠A = 43°
Let's find angle C
[tex]\frac{sin 43}{2. 5} = \frac{sinC}{3. 6}[/tex]
cross multiply
0. 682 × 3. 6 = sin C × 2. 5
sin C = 2. 4552/ 2. 5
C = [tex]sin^-^1( 0. 98206)[/tex]
C = 79. 11°
To find length of b
b = [tex]\sqrt{c^2 - a^2}[/tex]
substitute the values
b = [tex]\sqrt{3. 6^2 - 2. 5^2}[/tex]
b = [tex]\sqrt{12. 96 - 6. 25 }[/tex]
b = [tex]\sqrt{6. 71}[/tex]
Take square root
b = 2. 59 cm
To find angle B, we have
[tex]\frac{sin 43}{2. 5} = \frac{sin B}{2. 59}[/tex]
cross multiply
0. 682 × 2. 59= sin B × 2. 5
sin B = 0. 7066
B = [tex]sin^-^1 ( 0. 7066)[/tex]
B = 44. 9 °
Thus , the length of b and angle B and C are 2. 9cm, 44. 9 degrees and 79. 11 degrees respectively.
Learn more about sine rule here:
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