Chapter A.2, Problem 43AYU

To determine

Find the missing length $x$ and the missing angles $A,B$ and $C$ .

Answer to Problem 43AYU

The missing length is 67.5 units. The missing angles are $A={60}^0,B={95}^0$ and $C={25}^0$

Explanation of Solution

Given information:

Each pair of ${\Delta }^{\text{'}}s$ is similar. Find the missing length $x$ and the missing angles $A,B$ and $C$ .

  

  

Calculation:

Let us consider that the ${\Delta }^{\text{'}}s$ are similar.

Sothe ${\Delta }^{\text{'}}s$ are similar, corresponding angles are equal.

  $A={60}^0,B={95}^0$ and $C={25}^0$

The corresponding sides are proportional. Therefore we get

  $\begin{array}{l}\frac{20}{45}=\frac{30}{x}\\ 20x=1350\end{array}$

  $\begin{array}{l}x=\frac{1350}{20}\\ x=67\cdot 5\end{array}$

Hence the missing length is $\boxed{67\cdot 5units}$