Question

1. Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.a = 8 2 in.b= 13.0 in.C= 15.4 in.

Answer 1

Given,

`\begin{gathered} a=8.2\text{ in.} \\ b=13.0\text{ in.} \\ c=15.4\text{ in.} \end{gathered}`

Solution:

Use the law of cosines,

`\begin{gathered} A=arccos[((b^2+c^2-a^2))/((2bc))] \\ A=arccos[(13.0^2+15.4^2-8.2^2)/(2*13.0*15.4)] \\ A=34.2\text{ degrees} \end{gathered}`
`\begin{gathered} B=arccos[((a^2+c^2-b^2)/(2ac)] \\ B=arccos[(8.2^2+15.4^2-13.0^2)/(2*8.2*15.4)] \\ B=55.6\text{ degrees} \end{gathered}`
`\begin{gathered} C=180-(A+B) \\ C=180-(27.3+56.1) \\ C=90.2\text{ degrees} \end{gathered}`

Thus, the given option (A) is correct.