Question

question
in \\( \delta \mathrm{tuv}, \mathrm{m} \angle \mathrm{t}=98^{\circ} \\) and \\( \mathrm{m} \angle \mathrm{u}=25^{\circ} \\). which list
has the sides of \\( \delta \mathrm{tuv} \\) in order from longest to
shortest?
answer
\\( \bigcirc \mathrm{vt}, \mathrm{tu}, \mathrm{uv} \\)
\\( \bigcirc \mathrm{tu}, \mathrm{uv}, \mathrm{vt} \\)
\\( \bigcirc \mathrm{tu}, \mathrm{vt}, \mathrm{uv} \\)
\\( \bigcirc \mathrm{uv}, \mathrm{tu}, \mathrm{vt} \\)
\\( \bigcirc \mathrm{uv}, \mathrm{vt}, \mathrm{tu} \\)
\\( \bigcirc \mathrm{vt}, \mathrm{uv}, \mathrm{tu} \\)

Explanation:

Step1: Find the measure of angle V

In a triangle, the sum of interior angles is \(180^\circ\). So, \(m\angle V=180^\circ - m\angle T - m\angle U\).
Substitute \(m\angle T = 98^\circ\) and \(m\angle U = 25^\circ\) into the formula:
\(m\angle V=180^\circ - 98^\circ - 25^\circ = 57^\circ\)

Step2: Relate angles to sides

In a triangle, the longer side is opposite the larger angle. Let's identify the sides opposite each angle:

• Side opposite \(\angle T\) ( \(98^\circ\)) is \(UV\)
• Side opposite \(\angle U\) ( \(25^\circ\)) is \(VT\)
• Side opposite \(\angle V\) ( \(57^\circ\)) is \(TU\)

Now, order the angles from largest to smallest: \(m\angle T>m\angle V>m\angle U\) ( \(98^\circ > 57^\circ > 25^\circ\))

So, the sides opposite these angles (from longest to shortest) will be \(UV\) (opposite \(\angle T\)), \(TU\) (opposite \(\angle V\)), \(VT\) (opposite \(\angle U\))

Answer:

UV, TU, VT