Question

if $st = 16$, $tr = 9$, and $wu = 18$, find the length of $overline{vw}$. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.
answer attempt 1 out of 2
$vw=$

Explanation:

Step1: Find the third angle of the first triangle

In \(\triangle RST\), using the angle - sum property of a triangle (\(180^{\circ}\)), the third angle \(\angle T=180^{\circ}-(97^{\circ}+34^{\circ}) = 49^{\circ}\)

Step2: Prove the similarity of triangles

In \(\triangle RST\) and \(\triangle UWV\), \(\angle R=\angle U = 97^{\circ}\), \(\angle T=\angle W = 49^{\circ}\). So, \(\triangle RST\sim\triangle UWV\) (by AA similarity criterion)

Step3: Set up the proportion

Since the triangles are similar, \(\frac{ST}{WV}=\frac{TR}{WU}\)
Substitute \(ST = 16\), \(TR = 9\), and \(WU = 18\) into the proportion: \(\frac{16}{WV}=\frac{9}{18}\)

Step4: Solve for \(WV\)

Cross - multiply: \(9\times WV=16\times18\)
\(WV=\frac{16\times18}{9}\)
\(WV = 32\)

Answer:

\(32\)