Question

as a, b and c. calculate the missing side. estimate your
b) 8 m 5 cm
d) 13 in 4 in
f) $sqrt{10}$ cm $sqrt{9}$ cm

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). If we need to find a non - hypotenuse side, we can rewrite it as \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Solve for part b

Let the sides of the right - triangle be \(a = 5\mathrm{cm}\), \(b = 8\mathrm{cm}\). We want to find the hypotenuse \(c\). Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}=\sqrt{5^{2}+8^{2}}=\sqrt{25 + 64}=\sqrt{89}\approx9.43\mathrm{cm}\)

Step3: Solve for part d

Let the hypotenuse \(c = 13\mathrm{in}\) and one side \(a = 4\mathrm{in}\). We want to find the other side \(b\). Using the formula \(b=\sqrt{c^{2}-a^{2}}=\sqrt{13^{2}-4^{2}}=\sqrt{169 - 16}=\sqrt{153}\approx12.37\mathrm{in}\)

Step4: Solve for part f

Let \(a=\sqrt{6}\mathrm{cm}\), \(b=\sqrt{10}\mathrm{cm}\). We want to find the hypotenuse \(c\). Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}=\sqrt{(\sqrt{6})^{2}+(\sqrt{10})^{2}}=\sqrt{6 + 10}=\sqrt{16}=4\mathrm{cm}\)

Answer:

b) \(\sqrt{89}\mathrm{cm}\approx9.43\mathrm{cm}\); d) \(\sqrt{153}\mathrm{in}\approx12.37\mathrm{in}\); f) \(4\mathrm{cm}\)