What is the measure of the unknown angle?
1 answer:
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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)
