Chapter A.2, Problem 41AYU

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 41AYU

$x=4$ units, $A=90°,B=60°,\text{and}C=30°$.

Explanation of Solution

Given:

Calculation:

Because the triangles are similar, corresponding angles are equal. So $A=90°,B=60°,\text{and}C=30°$. Also, the corresponding sides are proportional. That is, $\frac{4}{8}=\frac{2}{x}$. Solve this equation for $x$.

$\frac{4}{8}=\frac{2}{x}$

Multiply both sides by $8x$.

$8x\times \frac{4}{8}=8x\times \frac{2}{x}$

$4x=16$

$x=4$ units.