Question

$△RST\sim △UAY$. In $△RST,RS=6cm,\angle S={50}^{\circ },ST=7.5cm$. The corresponding sides of $△RST$ and $△UAY$ are in the ratio $5:4$. Construct $△UAY$

Answer 1

Given that $△RST\sim △UAY$:
In $△RST,RS=6cm,\angle S={50}^{\circ },ST=7.5cm$
Given that the corresponding sides of $△RST$ and $△UAY$ are in the ratio $5:4$.
$\therefore \frac{RS}{UA}=\frac{ST}{UY}=\frac{RT}{UY}=\frac{5}{4}$
$\angle S=\angle A={50}^{\circ }$
$\therefore \frac{RS}{UA}=\frac{5}{4}$
$\therefore \frac{6}{UA}=\frac{5}{4}$
$\therefore UA=\frac{6\times 4}{5}$
$\therefore U=4.8cm$
Similarly, $\frac{ST}{AY}=\frac{5}{4}$
$\frac{7.5}{AY}=\frac{5}{4}$
$\therefore AY=\frac{7.5\times 4}{5}$
$\therefore AY=6cm$.
Therefore, in $△UAY,UA=4.8cm,AY=6cm$ and $\angle A={50}^{\circ }$