32.2k views
3 votes
Solve the following. List all possible possible solutions for the ambiguous case. #7

Solve the following. List all possible possible solutions for the ambiguous case. #7-example-1
User Namit
by
8.3k points

1 Answer

2 votes

The sum of the interior angles of any triangle is always 180º:


A+B+C=180

Use the equation above and the given data to find C:


\begin{gathered} C=180º-A-B \\ C=180º-38º-72º \\ C=70º \end{gathered}

Law of sines:


(a)/(sinA)=(b)/(sinB)=(c)/(sinC)

Use the pair of ratios for a and b to solve a:


\begin{gathered} (a)/(sinA)=(b)/(sinB) \\ \\ a=sinA*(b)/(sinB) \\ \\ a=sin38º*(12)/(sin72º) \\ \\ a=7.8 \end{gathered}

Use the pair of ratios for b and c to solve c:


\begin{gathered} (c)/(sinC)=(b)/(sinB) \\ \\ c=sinC*(b)/(sinB) \\ \\ c=sin70º*(12)/(sin72º) \\ \\ c=11.9 \end{gathered}Thenm, the solution for the given triangle is:A=38ºB=72ºC=70ºa=7.8b=12c=11.9
Solve the following. List all possible possible solutions for the ambiguous case. #7-example-1
User Dan Prince
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories