Question

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.

Answer 1

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!