Question

1. error analysis tia says that ∠q must be the largest angle in △qrs because 150 > 70 > 1.7. explain tia’s error.

Explanation:

Step1: Convert units

Convert \(1.7m\) to \(cm\). Since \(1m = 100cm\), then \(1.7m=1.7\times100 = 170cm\).

Step2: Compare side lengths

Now, the side lengths of \(\triangle QRS\) are \(QR = 70cm\), \(RS=150cm\), \(QS = 170cm\).

Step3: Apply triangle - angle relationship

In a triangle, the largest angle is opposite the longest side. The longest side is \(QS\), so the largest angle is \(\angle R\) (opposite \(QS\)), not \(\angle Q\). Tia's error was not converting the units of the side lengths to the same unit before comparing.

Answer:

Tia did not convert the units of the side lengths to the same unit. After converting \(1.7m\) to \(170cm\), the longest side is \(QS\) (\(170cm\)). In a triangle, the largest angle is opposite the longest side. So the largest angle is \(\angle R\) (opposite \(QS\)), not \(\angle Q\).