High School

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Nicole is flying two kites. She has 97 feet of string out to one kite and 115 feet out to the other kite. The angle formed by the two strings is 28 degrees. Find the distance between the kites.

Answer :

The distance between the two kites is approximately 145.8 feet.

The Law of Cosines is a trigonometric formula that relates the sides and angles of a triangle. Specifically, it relates the length of one side of a triangle to the other two sides and the angle between them

We can use the Law of Cosines to solve for the distance between the two kites. Let's call the distance between the kites "d".

From the problem statement, we have two sides of the triangle formed by the two strings (97 feet and 115 feet) and the included angle (28 degrees). We can use the Law of Cosines to solve for the third side

d^2 = 97^2 + 115^2 - 2(97)(115)cos(28)

Using a calculator, we get

d² ≈ 21251.4

Taking the square root of both sides, we get

d ≈ 145.8 feet

Learn more about Law of Cosines here

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