Question

determine the missing length in each right triangle using the pythagorean theorem. round the answer to the nearest tenth.
tu =
eg =
qr =

Explanation:

3. For triangle \(TSU\)

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 8\), \(b=9\), and \(c = TU\).

$$TU=\sqrt{8^{2}+9^{2}}$$

Step2: Calculate the squares

$$8^{2}=64$$

,

$$9^{2}=81$$

$$TU=\sqrt{64 + 81}=\sqrt{145}$$

Step3: Find the square - root

\(\sqrt{145}\approx12.0\)

4. For triangle \(FEG\)

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 3\), \(b = 17\), and \(c=EG\)

$$EG=\sqrt{3^{2}+17^{2}}$$

Step2: Calculate the squares

$$3^{2}=9$$

,

$$17^{2}=289$$

$$EG=\sqrt{9+289}=\sqrt{298}$$

Step3: Find the square - root

\(\sqrt{298}\approx17.3\)

5. For triangle \(PQR\)

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = QR\), \(b = 1\), and \(c = 5\)

$$QR=\sqrt{5^{2}-1^{2}}$$

Step2: Calculate the squares

$$5^{2}=25$$

,

$$1^{2}=1$$

$$QR=\sqrt{25 - 1}=\sqrt{24}$$

Step3: Find the square - root

\(\sqrt{24}\approx4.9\)

Answer:

\(TU\approx12.0\) yd, \(EG\approx17.3\) in, \(QR\approx4.9\) ft