Answer:
Part 1) It is not possible to apply the Pythagorean Theorem to find the missing side, because is not a right triangle
Part 2) I would use the law of the cosine, because to apply the law of sine I would need to know the value of angle C or angle B
Part 3) The length of side CB is [tex]369\ units[/tex]
Part 4) The measure of angle C is [tex]35\°[/tex]
Part 5) The measure of angle B is [tex]88\°[/tex]
Step-by-step explanation:
Part 1) Can you use Pythagorean Theorem to find the missing side?
we know that
The Pythagorean Theorem is used in a right triangle
The triangle ABC of the figure is not a right triangle
therefore
It is not possible to apply the Pythagorean Theorem to find the missing side
Part 2) Would you use Law of Sine or Law of Cosine to find the length of side CB?
I would use the law of the cosine, because to apply the law of sine I would need to know the value of angle C or angle B
Part 3) Find the length of side CB. Show your work and round your answer to the nearest whole number
Applying the law of cosine
[tex]BC^{2}=AB^{2}+AC^{2}-2(AB)(AC)cos(A)[/tex]
substitute the values
[tex]BC^{2}=255^{2}+440^{2}-2(255)(440)cos(57\°)[/tex]
[tex]BC^{2}=136,408[/tex]
[tex]BC=369\ units[/tex]
Part 4) Find the measure of angle C. (Hint: use the other “Law”). Round your answer to the nearest whole degree
Applying the law of sines
[tex]\frac{AB}{sin(C)}=\frac{CB}{sin(A)}[/tex]
substitute the values
[tex]\frac{255}{sin(C)}=\frac{369}{sin(57\°)}[/tex]
[tex]sin(C)=255*sin(57\°)/369=0.5796[/tex]
[tex]C=arcsin(0.5796)=35\°[/tex]
Part 5) What is the measure of angle B? Show your work and round your answer to the nearest whole degree.
Remember that
the sum of the interior angles of a triangle must be equal to 180 degrees
sp
[tex]<A+<B+<C=180\°[/tex]
substitute the values and solve for <B
[tex]57\°+<B+35\°=180\°[/tex]
[tex]<B=180\°-92\°=88\°[/tex]
