Question

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!!

Answer 1

We can make a drawing to see better:

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

$\begin{gathered} \tan a=\frac{MS}{RM}=\frac{TM}{MS} \\ TM=\frac{MS^2}{RM}=\frac{9^2}{4}=\frac{81}{4}=20.25 \end{gathered}$

The answer is TM = 20.25

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

$\begin{gathered} \sin b=\frac{RM}{RS}=\frac{RS}{RT} \\ RT=\frac{RS^2}{RM}=\frac{20^2}{8}=\frac{400}{8}=50 \end{gathered}$

The answer is RT = 50.

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

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

The answer is TS = 12.043

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

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

The answer is RT = 5/8 = 0.625