Answer:
A) = 23.0 miles
B) 14.4 Miles
Step-by-step explanation:
A) [tex]distance\ AD= x+y.\\ First\ find\ the\ value\ of\ x\ and\ z,\ then\ use\ the\ value\\ \\ yz\ to\ get\ the\ value\ of\ y\\ cos60\textdegree\ =\frac{21}{hy}=\frac{x}{10}[/tex]
[tex]sin60\textdegree\ =\frac{opp}{hyp}=\frac{z}{10}[/tex]
[tex]z=10\times sin60\textdegree =10\times 0.8660=8.66\ miles[/tex]
[tex]use\ pythagores\ theorem\ to\ get\ the\ value\ of\ y.\ l,e[/tex]
[tex]y=\sqrt{{20}^2-z^2}=\sqrt{{20}^2-{8.66}^2}=\sqrt{325.0044}[/tex]
[tex]=18.03\ miles[/tex]
[tex]\therefore\ distance\ AD=5+18.03[/tex]
[tex]=23.03\\ 23.0\ miles[/tex]
B) [tex]Ansween\ 14.4\ Miles[/tex]
[tex]< ABN=\varphi=30\textdegree\ \{Beary\ 4A\ from\ B=360\textdegree\ -60\textdegree\ =300\textdegree\}[/tex]
[tex]AB=y.[/tex]
[tex]\cos{\theta=\frac{ads}{h}p}\\ cos\ G\begin{matrix}0\\0\\\end{matrix}=\frac{x}{25}[/tex]
[tex]x=25\times cos\ 60\textdegree[/tex]
[tex]=12.5\ mle[/tex]
[tex]cos\ 30\textdegree=\frac{xe}{y}=\frac{12.5}{y}[/tex]
[tex]\because\ y=\frac{12.5}{cos\ 30\textdegree}[/tex]
[tex]=14.Fmm'_\mathcal{i}(es[/tex]
I hope this helps you
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