The figure below shows a bamboo structure. What is the length of CN, rounded to the nearest hundredth? Show all the steps you used to find your answer.
We are going to use three equations we can derive from the picture. All relate to right triangles and the pythagorean theorem. For simplicity, let BC = x, CA=y, and CN=d. We also know that BN=6 and NC=5, <ANC=90, <BNC=90, and <BCA=90. (1) x^2+y^2=11^2 (big triangle, all outer edges) (2) 5^2+d^2=y^2 (smaller, upper triangle) (3) 6^2+d^2=x^2 (smaller bottom triangle) Since (2) and (3) are solved for y^2 and x^2 respectively, we can plug (2) and (3) into (1) replacing those terms with their equations: 6^2+d^2+5^2+d^2=11^2 2d^2+36+25=121 (simplified) 2d^2=60 d^2=30 d=5.48 HTH!
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