Chapter A.2, Problem 43AYU

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 43AYU

$x=67.5$ units, $A=60°,B=95°,\text{and}C=25°$.

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, $\frac{20}{30}=\frac{45}{x}$. Solve this equation for $x$.

$\frac{20}{30}=\frac{45}{x}$

Multiply both sides by $30x$.

$30x\times \frac{20}{30}=30x\times \frac{45}{x}$

$20x=1350$

$x=67.5$ units.