Question

question
video examples
if ( s t = 34, t r = 30 ), and ( w u = 6 ),
find the length of ( overline { v w } ). round your
answer to the nearest tenth if necessary.
figures are not necessarily drawn to scale.
answer
attempt 2 out of 3
( v w = )

Explanation:

Step1: Find the third angle of each triangle

In \(\triangle STR\), using the angle - sum property of a triangle (\(180^{\circ}\)), the third angle \(\angle R=180^{\circ}-(97^{\circ}+38^{\circ}) = 45^{\circ}\).
In \(\triangle VWU\), the third angle \(\angle W=180^{\circ}-(38^{\circ}+45^{\circ})=97^{\circ}\).

Step2: Prove the similarity of triangles

Since \(\angle S=\angle V = 38^{\circ}\), \(\angle T=\angle W = 97^{\circ}\), and \(\angle R=\angle U = 45^{\circ}\), by the AA (Angle - Angle) similarity criterion, \(\triangle STR\sim\triangle VWU\).

Step3: Set up the proportion

For similar triangles \(\triangle STR\) and \(\triangle VWU\), the ratios of corresponding sides are equal. That is \(\frac{ST}{VW}=\frac{TR}{WU}\).
Substitute \(ST = 34\), \(TR = 30\), and \(WU = 6\) into the proportion: \(\frac{34}{VW}=\frac{30}{6}\).

Step4: Solve for \(VW\)

Cross - multiply: \(30\times VW=34\times6\).
Then \(30VW = 204\).
Divide both sides by 30: \(VW=\frac{204}{30}=6.8\).

Answer:

\(6.8\)