The measurements of $ riangle LMN$ and $ riangle ABC$ are shown in the figure given below. The length of side AC is:

[IMAGE_1]

Question

The measurements of $	riangle LMN$ and $	riangle ABC$ are shown in the figure given below. The length of side AC is:

[IMAGE_1]

Accepted Answer

Step 1: $	riangle LMN \sim 	riangle ABC$ (AA similarity, $\angle M = \angle B = 130°$, $\angle N = \angle C = 28°$, so $\angle L = \angle A = 22°$). $\frac{LM}{AB} = \frac{MN}{BC}$. $\frac{45}{5} = \frac{63}{BC}$. Wait — by corresponding sides: $\frac{LM}{AB} = \frac{LN}{AC}$, so $\frac{45}{5} = \frac{72}{AC} \Rightarrow AC = 8$ cm.

Question

Solution