Chapter 8.6, Problem 2BCYP

To determine

To calculate: The value of x to the nearest degree.

Answer to Problem 2BCYP

The required value of x is $31°$ .

Explanation of Solution

Given Information:

The given triangle is

  

Formula Used:

Law of sine

  $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

Here $A,B\text{and}C$ are the angles and $a,b\text{and}c$ are the sides.

Consider the angle $R$ is $x°$ whose opposite side length is 6.8.

Similarly, the angle $T$ is $24°$ whose opposite side length is 5.3.

Now, find $x°$ . Use law of sine.

  $\begin{array}{c}\frac{\sin 24}{5.3}=\frac{\sin x}{6.8}\\ \sin x=\frac{6.8\times \sin 24}{5.3}\\ x=31.4564\dots \\ x\approx 31°\end{array}$

Hence, the required value of x is $31°$ .