Question

A triangle has points dallas, destination 1, and destination 2. the distance from dallas to destination 1 is 720 miles, and the distance from destination 1 to destination 2 is 290 miles. the angle formed between dallas, destination 1, and destination 2 is 125 degrees. 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

Answer 1

The distance from the second destination back to Dallas is 918 miles

Given

A triangle has points Dallas, destination 1, and destination 2.

The distance from Dallas to destination 1 is 720 miles

The distance from destination 1 and destination 2 is 290 miles

the angle formed between Dallas, destination 1, and destination 2 is 125 degrees.

He moves from destination 1 to Dallas then destination 2

We could use cosine law to find the distance

What is cosine law?

The Law of cosines or cosine law means the relation between the length of sides of a triangle with respect to the cosine of its angle. It is also called the cosine rule

$b^{2}=a^2+c^2-2ac*cosB$

=$290^2+720^2-2*720*290*cos125$

=84100+518400-417600 cos 125

=602500-417600*(-0.5735)

=602500+239493.6

=841993.6

b=917.6 miles

≅918 miles

The distance is 918 miles  he will fly from the second destination back to Dallas

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