Question

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.)
PLEASE HELP ASAP!

Answer 1

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)