Chapter A.2, Problem 42AYU

To determine

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

Answer to Problem 42AYU

The missing length is 8units. The angles are $A={30}^0,B={75}^0,C={75}^0$

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 two ${\Delta }^{\text{'}}s$ are similar if the corresponding angles are equal and length of the corresponding sides are proportional.

It is given that the ${\Delta }^{\text{'}}s$ are similar , the corresponding angles are equal. Hence we get angles

  $A={30}^0,B={75}^0,C={75}^0$

We know that the corresponding sides of similar ${\Delta }^{\text{'}}s$ are proportional. Thus

  $\frac{12}{6}=\frac{16}{x}$

Solve the equation for $x$

  $x\left(\frac{12}{6}\right)=x\left(\frac{16}{x}\right)$

  $2x=16$

Divide both sides by 2.

  $\frac{2x}{2}=\frac{16}{2}$

Hence the missing length is 8 units. The angles are

  $A={30}^0,B={75}^0,C={75}^0$