Questions: Calculer la longueur manquante dans chacun des triangles les suivants. Si besoin, arrondir le résultats au centième.

Solution Steps

All the triangles in the problem are right-angled triangles.

For right-angled triangles, the Pythagorean Theorem states that \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\) and \(b\) are the other two sides.

For Triangle 1:

• Given: \(a = 2 \text{ cm}\), \(c = 7 \text{ cm}\)
• Find: \(b\)

Using the Pythagorean Theorem: \[ a^2 + b^2 = c^2 \] \[ 2^2 + b^2 = 7^2 \] \[ 4 + b^2 = 49 \] \[ b^2 = 45 \] \[ b = \sqrt{45} \approx 6.71 \text{ cm} \]

For Triangle 2:

• Given: \(a = 1.8 \text{ m}\), \(c = 4.7 \text{ m}\)
• Find: \(b\)

Using the Pythagorean Theorem: \[ a^2 + b^2 = c^2 \] \[ 1.8^2 + b^2 = 4.7^2 \] \[ 3.24 + b^2 = 22.09 \] \[ b^2 = 18.85 \] \[ b = \sqrt{18.85} \approx 4.34 \text{ m} \]

For Triangle 3:

• Given: \(a = 3 \text{ cm}\), \(c = 5 \text{ cm}\)
• Find: \(b\)

Using the Pythagorean Theorem: \[ a^2 + b^2 = c^2 \] \[ 3^2 + b^2 = 5^2 \] \[ 9 + b^2 = 25 \] \[ b^2 = 16 \] \[ b = \sqrt{16} = 4 \text{ cm} \]

Final Answer