Question

find the shortest side of δstu. s 2y - 98° t y - 17° u y - 21°

Explanation:

Step1: Sum of angles in triangle

The sum of interior angles in a triangle is \(180^\circ\). So, \((2y - 98^\circ)+(y - 17^\circ)+(y - 21^\circ)=180^\circ\).

Step2: Solve for \(y\)

Combine like terms: \(2y - 98 + y - 17 + y - 21 = 180\) → \(4y - 136 = 180\). Add 136 to both sides: \(4y = 316\). Divide by 4: \(y = 79\).

Step3: Find each angle

• \(\angle S = 2(79)-98 = 158 - 98 = 60^\circ\)
• \(\angle T = 79 - 17 = 62^\circ\)
• \(\angle U = 79 - 21 = 58^\circ\)

Step4: Relate angles to sides

In a triangle, the shortest side is opposite the smallest angle. \(\angle U = 58^\circ\) (smallest), so the side opposite \(\angle U\) is \(ST\).

Answer:

The shortest side of \(\triangle STU\) is \(ST\).