Question

find the missing side of each triangle. round your answers to the nearest tenth if necessary.

Explanation:

Step1: Apply Pythagorean theorem for 1)

For a right - triangle with legs \(a = 6\) and \(b=8\) and hypotenuse \(x\), by the Pythagorean theorem \(a^{2}+b^{2}=x^{2}\). So \(x^{2}=6^{2}+8^{2}=36 + 64=100\), then \(x=\sqrt{100}=10\) cm.

Step2: Apply Pythagorean theorem for 2)

For a right - triangle with hypotenuse \(c = 5\) and one leg \(b = 4\), and the other leg \(x\). By the Pythagorean theorem \(x^{2}+b^{2}=c^{2}\), so \(x^{2}=c^{2}-b^{2}\). Substitute \(c = 5\) and \(b = 4\), we get \(x^{2}=5^{2}-4^{2}=25 - 16 = 9\), then \(x=\sqrt{9}=3\) km.

Step3: Apply Pythagorean theorem for 3)

For a right - triangle with legs \(a = 4\) and \(b=x\) and hypotenuse \(c = 9\). By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\). Substitute \(a = 4\) and \(c = 9\), we get \(x^{2}=9^{2}-4^{2}=81-16 = 65\), then \(x=\sqrt{65}\approx 8.1\) ft.

Step4: Apply Pythagorean theorem for 4)

For a right - triangle with legs \(a = 5\) and \(b = 8\) and hypotenuse \(x\). By the Pythagorean theorem \(a^{2}+b^{2}=x^{2}\). Substitute \(a = 5\) and \(b = 8\), we get \(x^{2}=5^{2}+8^{2}=25 + 64=89\), then \(x=\sqrt{89}\approx 9.4\) km.

Answer:

1. \(10\) cm
2. \(3\) km
3. \(8.1\) ft
4. \(9.4\) km