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Mathematics

OpenStudy (anonymous):

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.

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OpenStudy (anonymous):

OpenStudy (anonymous):

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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