Question

value: 2
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 \(a = 8.4\), \(b = 10.3\), and \(c=x\).
\[x^{2}=8.4^{2}+10.3^{2}\]

Step2: Calculate the squares

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

Step3: Find \(x\)

\[x=\sqrt{176.65}\approx 13.3\]

Answer:

d. 13.3 yd