Question

1. what is ab?

Explanation:

Step1: Identify similar triangles

Since the angles of $\triangle ABC$ and $\triangle FGH$ are $37^{\circ}$, $53^{\circ}$ and $90^{\circ}$, the two triangles are similar.

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. Let $AB = x$. We have $\frac{AB}{FG}=\frac{BC}{GH}$. We know $FG = 6$ in, $BC = 8$ in and $GH = 10$ in. So $\frac{x}{6}=\frac{8}{10}$.

Step3: Solve for $x$

Cross - multiply: $10x=6\times8 = 48$. Then $x=\frac{48}{10}=4.8$ in.

Answer:

$4.8$ in