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You fly a hot air balloon 0.5 miles above the ground. What is the measure of BD⌢, the portion of Earth that you can see? Round your answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)

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You fly a hot air balloon 05 miles above the ground What is the measure of BD the portion of Earth that you can see Round your answer to the nearest tenth Earth class=

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Step-by-step explanation:

To solve this problem, we need the angle CAD, which can then be used to calculate the arc BD.

From definition of cosine,

cos(x) = adjacent / hypotenuse

cos(x) = AD / AC = 4000 / 4000.5 = 0.9998750156230471

The inverse function gives

x = arccosine (4000/4000.5)

  = arccosine (0.9998750156230471)

  = 0.01581056485742214 radians = 0.9058786380481468 degrees

Radius of the earth, r = 4000 miles

Arc BD = 2 time arc subtended by angle x

= 2 (rx)    where x is in radians

= 2*4000*0.01581056485742214

= 126.48 miles (to two decimal places)

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