Question

round your answers to the nearest tenth if necessary.
2)
4 km
5 km
4)
5 km
8 km

Explanation:

Step1: Apply Pythagorean theorem for problem 2

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 5\) km, \(a=4\) km, \(b = x\).
\(x^{2}+4^{2}=5^{2}\)
\(x^{2}=25 - 16\)
\(x^{2}=9\)
\(x = 3\) km

Step2: Apply Pythagorean theorem for problem 4

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(a = 5\) km, \(b=8\) km, \(c=x\).
\(x^{2}=5^{2}+8^{2}\)
\(x^{2}=25 + 64\)
\(x^{2}=89\)
\(x=\sqrt{89}\approx9.4\) km

Answer:

For problem 2: \(x = 3\) km. For problem 4: \(x\approx9.4\) km.