311,378 views
19 votes
19 votes
Please help me with these questions!! this is due at 11:59 pm EST. If you could explain how you got your answers too, that would be so helpful!! (please show your work)use the right triangle ️RST and the given information to solve each problem. 7. Find TM if RM = 4 and MS = 9 8. Find RT if RS = 20 and RM = 8 9. Find TS if RM = 5 and MS = 7 10. Find RT if RM = 1/2 and MS = 1/4 thank you so much if you can help me!!

Please help me with these questions!! this is due at 11:59 pm EST. If you could explain-example-1
User LWZ
by
2.9k points

1 Answer

20 votes
20 votes

We can make a drawing to see better:

7) We know that RM = 4 and MS = 9, so:


\begin{gathered} \tan a=(MS)/(RM)=(TM)/(MS) \\ TM=(MS^2)/(RM)=(9^2)/(4)=(81)/(4)=20.25 \end{gathered}

The answer is TM = 20.25

8) We know that RS = 20 and RM = 8, so:


\begin{gathered} \sin b=(RM)/(RS)=(RS)/(RT) \\ RT=(RS^2)/(RM)=(20^2)/(8)=(400)/(8)=50 \end{gathered}

The answer is RT = 50.

9) We know that RM = 5 and MS = 7, so:


\begin{gathered} \tan b=(RM)/(MS)=(RS)/(TS) \\ TS=RS\cdot(MS)/(RM) \\ RS=\sqrt[]{RM^2+MS^2} \\ TS=\sqrt[]{RM^2+MS^2}\cdot(MS)/(RM) \\ TS=\sqrt[]{5^2+7^2}\cdot(7)/(5)=\sqrt[]{25+49}\cdot(7)/(5) \\ TS=\sqrt[]{74}\cdot(7)/(5)\approx12.043 \end{gathered}

The answer is TS = 12.043

10) We know that RM = 1/2 and MS = 1/4, so:


\begin{gathered} \sin b=(RM)/(RS)=(RS)/(RT) \\ RT=(RS^2)/(RM)=(RM^2+MS^2)/(RM) \\ RT=(((1)/(2))^2+((1)/(4))^2)/((1)/(2))=2\cdot((1)/(4)+(1)/(16)) \\ RT=2\cdot(4+1)/(16)=(5)/(8)=0.625 \end{gathered}

The answer is RT = 5/8 = 0.625

Please help me with these questions!! this is due at 11:59 pm EST. If you could explain-example-1
User Bribles
by
2.7k points