Question

the missing side of each triangle. leave your a
a) \\( \sqrt { 62 } \mathrm { km } \\)
b) \\( \sqrt { 10 } \mathrm { km } \\)
c) \\( 2 \sqrt { 22 } \mathrm { km } \\)
d) \\( 7 \sqrt { 2 } \mathrm { km } \\)

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(a = \sqrt{26}\), \(b = 6\), and \(c=x\). So, \(x^{2}=(\sqrt{26})^{2}+6^{2}\).

Step2: Calculate the value of \(x^{2}\)

\((\sqrt{26})^{2}=26\) and \(6^{2}=36\). Then \(x^{2}=26 + 36\).

Step3: Simplify the right - hand side

\(x^{2}=62\).

Step4: Solve for \(x\)

Take the square root of both sides, \(x=\sqrt{62}\).

Answer:

A. \(\sqrt{62}\text{ km}\)