Problem

1. Isabelle is flying a kite on a windy day. When the kite is $15 \mathrm{~m}$ above ground, it makes an angle of $50^{\circ}$ with the horizontal. If Isabelle is holding the string $1 \mathrm{~m}$ above the ground, how much string has she released? Round your answer to the nearest metre.

Answer

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Answer

Round L to the nearest meter: \(\boxed{14}\)

Steps

Step 1 :Let the length of the string be L, the height of the kite be H, and the angle of elevation be A. We have: \(\tan(A) = \frac{H}{L - 1}\)

Step 2 :Given A = 50 degrees and H = 15 m, we need to find L.

Step 3 :Convert A to radians: \(A_{rad} = 0.8726646259971648\)

Step 4 :Using the tangent function, we get: \(L = 13.5864944676592\)

Step 5 :Round L to the nearest meter: \(\boxed{14}\)

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