Chapter A.2, Problem 42AYU

To determine

To find: The missing length $x$ and the missing angles $A,B,\text{and}C$ if the triangles in each pair are similar.

Answer to Problem 42AYU

$x=8$ units, $A=30°,B=75°,\text{and}C=75°$.

Explanation of Solution

Given:

Calculation:

Because the triangles are similar, corresponding angles are equal. So $A=30°,B=75°,\text{and}C=75°$. Also, the corresponding sides are proportional. That is, $\frac{12}{6}=\frac{16}{x}$. Solve this equation for $x$.

$\frac{12}{6}=\frac{16}{x}$

Multiply both sides by $6x$.

$6x\times \frac{12}{6}=6x\times \frac{16}{x}$

$12x=96$

$x=8$ units.