Question

solve for x. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.
answer attempt 1 out of 2
x = submit answer

Explanation:

Step1: Find the third angle of the first triangle

In \(\triangle STU\), using the angle - sum property of a triangle (\(A + B + C=180^{\circ}\)). Let the third angle be \(A\), then \(A = 180-(63 + 72)=45^{\circ}\).

Step2: Prove the similarity of triangles

Since in \(\triangle STU\) and \(\triangle V WX\), \(\angle S=\angle V = 63^{\circ}\), \(\angle U=\angle X = 45^{\circ}\), by the AA (angle - angle) similarity criterion, \(\triangle STU\sim\triangle V WX\).

Step3: Set up the proportion

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{ST}{VX}=\frac{SU}{VW}\). Substituting \(ST = 13\), \(SU = 17\), \(VW = 16\), and \(VX=x\), we get \(\frac{13}{x}=\frac{17}{16}\).

Step4: Solve for \(x\)

Cross - multiply: \(17x=13\times16\). Then \(x=\frac{13\times16}{17}\). Calculate \(13\times16 = 208\), and \(x=\frac{208}{17}\approx12.2\).

Answer:

\(12.2\)