Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Two planes leave the airport at the same time. In one hour the plane that has flown north has traveled 400 miles. The plane that has flown southwest has traveled 250 miles. How far apart are the planes?
LAW OF COSINES
GEOMETRY

Sagot :

kate200468
[tex]a^2=b^2+c^2-2\cdot b\cdot c\cdot cos \alpha \\---------------\\\\x^2=250^2+400^2-2\cdot250\cdot400\cdot cos135^0\\\\x^2=62,500+160,000-200,000\cdot cos(180^0-45^0)\\\\x^2=222,500-200,000\cdot(-cos45^0)\\\\x^2=222,500-200,000\cdot \frac{ \sqrt{2} }{2} \\\\x^2=222,500+100,000\cdot \sqrt{2} \\\\x^2=2500\cdot(89+40 \sqrt{2} )\\\\[/tex]

[tex]x=50\cdot \sqrt{89+40 \sqrt{2}} \ \ \ \Rightarrow\ \ \ x\approx603.26\ [miles]\\\\Ans.\ the\ distance\ is\ about\ 603.26\ miles[/tex]
View image kate200468
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.