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A plane takes off from an airport on the bearing S 29°W. It continues for 20 minutes then changes to bearing S 52°W and flies for 2 hours 20 minutes on this course then lands at a second airport. If the plane's speed is 420 mph, how far from the first airport is the second airport? Round to the nearest mile.
A. 1011 mi
B. 1111 mi
C. 1010 mi
D. 1110 mi

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Answer: 1110 miles

Step-by-step explanation:

Given that :

Speed (V) = 420 mph

t1 = 20 minutes = 20/60 = 0.3333 hour

t2 = 2 hours 20 minutes = 2.333 hours

Distance = speed * time

d1 = 420 * 0.333 = 140 miles

d2 = 420 * 2.33333 = 979.98 = 980 miles

Using cosine rule :

x = sqrt(d1² + d2² - 2(d1 * d2) cos 157

x = sqrt(140^2 + 980^2 - 2(140 * 980) cos157

x = sqrt(1232586.5)

x = 1110.2191

x = 1110 miles

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