Question

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find the longest side of δrst.
t
2y
r
y+38°
s
73°
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Explanation:

Step1: Sum of angles in triangle

The sum of interior angles in a triangle is \(180^\circ\). So, \(2y+(y + 38^\circ)+73^\circ=180^\circ\).

Step2: Solve for y

Combine like terms: \(3y+111^\circ = 180^\circ\). Subtract \(111^\circ\) from both sides: \(3y=180^\circ - 111^\circ=69^\circ\). Divide by 3: \(y = 23^\circ\).

Step3: Find each angle

• Angle \(T\): \(2y=2\times23^\circ = 46^\circ\)
• Angle \(R\): \(y + 38^\circ=23^\circ+38^\circ = 61^\circ\)
• Angle \(S\): \(73^\circ\)

Step4: Determine longest side

In a triangle, the longest side is opposite the largest angle. The largest angle is \(73^\circ\) (angle \(S\)), so the side opposite angle \(S\) is \(RT\).

Answer:

The longest side of \(\triangle RST\) is \(RT\) (the side opposite the \(73^\circ\) angle).