Respuesta :
The length 2.3 and 7.8 units
We have given that ΔABC, c = 5. 4, a = 3. 3, and measure of angle A = 20 degrees.
What is the formula for low of cosine?
The Law of Cosines, which tells us
[tex]a^{2}=b^{2} +c^{2} -2bccosA[/tex]
giving us a quadratic equation for b we can solve. But let's do it with the Law of Sines as asked.
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
We have c,a,A so the Law of Sines gives us sin C
[tex]sinC=\frac{csina}{a} =\frac{5.4sin20}{3.3} =0.5597[/tex]
There are two possible triangle angles with this sine, supplementary angles, one acute, one obtuse
[tex]C_{a}=arcsin(0.5597)=34.033^{0}[/tex]
[tex]C_{0}=180-C_{a} =145.96^0[/tex]
Both of these make a valid triangle with A=20°. They give respective B's:
[tex]B_{a}=180-A-C_{a} =125.96^0[/tex]
[tex]B_{0}=180-C_{0} =14.033^0[/tex]
So we get two possibilities for b:
[tex]b=\frac{asinB}{sinA} \\\\b_{a} =\frac{3.3sin125.96}{sin 20} \\\\b_{a}=7.8\\\\ b_0=2.3[/tex]
2.3 units and 7.8 units
Therefore we get the length 2.3 and 7.8 units
To learn more about the low of sine and cosine visit:
https://brainly.com/question/4372174
Answer: 2.3 units and 7.8 units
Let's check it with the Law of Cosines:
There's a shortcut for the quadratic formula when the middle term is 'even.'
Looks good.
