Question

find the length of the missing side using the pythagorean theorem. round to the nearest tenth if necessary. 10.3 yd x 8.4 yd a. 21.7 yd b. 6.7 yd c. 15.8 yd d. 13.3 yd

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here \(a = 8.4\) and \(b=10.3\), and we want to find \(c=x\).
\[x^{2}=8.4^{2}+ 10.3^{2}\]

Step2: Calculate squares

\[8.4^{2}=70.56\] and \[10.3^{2}=106.09\]
So \(x^{2}=70.56 + 106.09=176.65\)

Step3: Find \(x\)

\[x=\sqrt{176.65}\approx13.3\]

Answer:

d. 13.3 yd