Question

applying the law of cosines to navigation
dallas 720 mi destination 1
125° 290 mi
destination 2
a pilot flies 720 miles from dallas, texas, to his first destination. after dropping off his cargo, he flies southeast 290 miles to his second destination. if the angle formed by his trip is 125°, what is the distance he will fly from the second destination back to dallas?
490 miles
918 miles
1,010 miles
842,026 miles

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \( c^{2}=a^{2}+b^{2}-2ab\cos C\), where \(a = 720\), \(b = 290\), and \(C=125^{\circ}\).

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step3: Solve for \(c\)

Take the square root of \(c^{2}\), \(c=\sqrt{842100.77}\approx918\)

Answer:

918 miles