(This is a "show your work" type of assignment)1. Can you use Pythagorean Theorem to find the missing side? Why or why not?2. Would you use Law of Sine or Law of Cosine to find the length of side CB? Explain your answer.3. Find the length of side CB. Show your work and round your answer to the nearest whole number.4. Find the measure of angle C. (Hint: use the other “Law”). Round your answer to the nearest whole degree. 5. What is the measure of angle B? Show your work and round your answer to the nearest whole degree.

Answer:Part 1) It is not possible to apply the Pythagorean Theorem to find the missing side, because is not a right trianglePart 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 BPart 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 thatThe Pythagorean Theorem is used in a right triangleThe triangle ABC of the figure is not a right trianglethereforeIt is not possible to apply the Pythagorean Theorem to find the missing sidePart 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 numberApplying 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 degreeApplying 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 thatthe sum of the interior angles of a triangle must be equal to 180 degreessp[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]