Question

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

918 miles is the answer

Answer 2

B) 918 miles

Explanation:

Here with I have attached the figure of the story.

Here we need to find side c, which represents distance from the second destination back to Dallas.

We have to use the cosine formula to find the missing side.

If we are given two sides and one included angle, we can use the cosine formula and find the missing side.

a = 720, b = 290 and ∠C =125°

`c^2 = a^2 + b^2 - 2ab cos C`

Now plug in the given values and simplify.

`c^2 = {720}^2 + 290^2 - 2*720*290 cos 125`

`c^2 = 518400 + 84100 - 417600 cos125`

`c^2 = 602500 - (-239,525.5)\\c^2 = 602500 + 239,525.5\\c^2 = 842025.5`

Taking the square root on both sides, we get

c = 917.6

Which is equivalent to 918 miles (rounded off to the nearest whole number)