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A hot-air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles are found to be 14° and 10°. How high is the balloon?

Answer :

Answer:0.602 mile

Explanation:

Given

balloon is Floating above a straight road

Angle of two consecutive mileposts on the road are [tex]14^{\circ}[/tex] and [tex]10^{\circ}[/tex]

Form Diagram

[tex]\tan 14=\frac{y}{x}[/tex]

[tex]y=x\tan 14[/tex]------1

Also

[tex]\tan 10=\frac{y}{x+1}[/tex]

[tex]y=(x+1)\tan 10[/tex] -----2

from 1 & 2 we get

[tex]x\tan 14=(x+1)\tan 10[/tex]

[tex]x\cdot \frac{\tan 14}{\tan 10}=x+1[/tex]

[tex]1.414 x=x+1[/tex]

[tex]0.414x=1[/tex]

[tex]x=2.41 miles[/tex]

Thus using 1 we get

[tex]y=2.41\times \tan 14=0.602 mile[/tex]    

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