Distance to A= 119mi
Disy¿tance to C=77mi
angle=34.6°
We have to find h, the angle that curts h will be half of 34.6, is a bisector
Using trigonometric to find h:
[tex]Cos(\theta)=\frac{c.a}{119mi}=\frac{h}{119mi}[/tex]
Isolating h:
[tex]\begin{gathered} cos(\frac{34.6}{2})*119mi=h \\ \\ h=113.61 \end{gathered}[/tex]
Using the Pythagorean theorem we calculate x:
[tex]\begin{gathered} 119^2=h^2+x^2 \\ x=\sqrt[\placeholder{⬚}]{119^2-h^2}=\sqrt[\placeholder{⬚}]{119^2-113.6^2}=35.4 \end{gathered}[/tex]
Now, we will use tan function:
[tex]\begin{gathered} tan\theta=\frac{b-x}{h} \\ \\ h*tan\theta=b-x \\ \\ b=h*tan\theta+x=113.61*tan(\frac{34.6}{2})+35.4=70.78 \end{gathered}[/tex]
The answer is: 70.78 mi.
