Question

segment ad is an altitude of triangle abc. if ad = 12, dc = 5, and ac = 13, find ba. round to the tenths place if necessary. 33.4 31.2 5.4

Explanation:

Step1: Use the geometric - property of similar triangles

Triangles ABD and CAD are similar (by AA similarity since $\angle ADB=\angle CDA = 90^{\circ}$ and $\angle B+\angle BAD = 90^{\circ}$, $\angle BAD+\angle CAD=90^{\circ}$, so $\angle B=\angle CAD$). Then, the ratios of corresponding sides are equal, i.e., $\frac{BA}{AC}=\frac{AC}{DC}$.

Step2: Substitute the given values

We know that $AC = 13$ and $DC = 5$. Let $BA=x$. From $\frac{x}{13}=\frac{13}{5}$.

Step3: Solve for $BA$

Cross - multiply to get $5x=13\times13$. Then $x=\frac{169}{5}=33.8$.

Answer:

33.8