Answer:
Height of the balloon is 6.923 miles or 11141.46m
Explanation:
We form two triangles with a common vertex so the relation of the angles is and the position both are measuring
[tex]tan(27)=\frac{Op}{Ad}\\Op1=Ad*Tan(27)\\Op1=Ad*0.595[/tex]
The second triangle have the mileposts on the road  that is a mile more so:
[tex]tan(24)=\frac{Op}{Ad+1mile} \\Op=tan(24)*(Ad+1mile)\\Op=0.445*(Ad+1mile)[/tex]
[tex]Op=0.445*Ad+0.445[/tex]
Now resolve the both equation to know the opposite side that is the height of the hot air balloon
[tex]Op*0.595=Op*0.4452+0.4452\\Op*(0.595-0.4452)=0.4452\\Op*0.0643=0.4452\\Op=\frac{0.4452}{0.0643}[/tex]
[tex]Op=6.923 mile[/tex]
Height=6.923miles
Leigth can be find also
[tex]Ad=tan(27)*6.923\\Ad=3.52 miles[/tex]
The measure can be express in meters so
[tex]6.923miles*\frac{1.60934km}{1mile}=11.4146km\\11.14146km*\frac{1000m}{1km}=11141.4608 m[/tex]
