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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 of depression are found to be 18° and 21°. How high is the balloon? (Round your answer to one decimal place.)

Respuesta :

Answer:

[tex]H = 2.1 mile[/tex]

Explanation:

Let the height of the balloon is H

so we will have

[tex]tan\theta_1 = \frac{H}{d}[/tex]

[tex]tan18 = \frac{H}{d}[/tex]

now after a mile post the angle is 21 degree

so we will have

[tex]tan 21 = \frac{H}{d - 1}[/tex]

so we have

[tex]d = \frac{H}{tan18}[/tex]

[tex]d = 3.08 H[/tex]

also we have

[tex]d - 1 = \frac{H}{tan21}[/tex]

[tex]3.08 H - 1 = 2.6 H[/tex]

[tex]H = 2.1 mile[/tex]

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