Question

mrs. blackburn is teaching a 5th grade class. she is standing 5.5 meters in front of tanvi. gabrielle is sitting to tanvis right. if gabrielle and mrs. blackburn are 8.6 meters apart, how far apart are tanvi and gabrielle? if necessary, round to the nearest tenth. meters submit

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 5.5\) (distance between Mrs. Blackburn and Tanvi), \(c=8.6\) (distance between Gabrielle and Mrs. Blackburn). We want to find \(b\) (distance between Tanvi and Gabrielle). The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 5.5\) and \(c = 8.6\) into \(b^{2}=c^{2}-a^{2}\). Then \(b^{2}=8.6^{2}-5.5^{2}\). Calculate \(8.6^{2}=73.96\) and \(5.5^{2}=30.25\). So \(b^{2}=73.96 - 30.25=43.71\).

Step3: Find \(b\)

Take the square root of \(b^{2}\), \(b=\sqrt{43.71}\approx6.6\)

Answer:

\(6.6\)