Chapter 8.6, Problem 2ACYP

To determine

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

Answer to Problem 2ACYP

The required value of x is $6°$ .

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 $W$ is $63°$ whose opposite side length is 125.

Similarly, the angle $T$ is $x°$ whose opposite side length is 14.

Now, find $x°$ . Use law of sine.

  $\begin{array}{c}\frac{\sin 63}{125}=\frac{\sin x}{14}\\ \sin x=\frac{14\times \sin 63}{125}\\ x=5.7272\dots \\ x\approx 6°\end{array}$

Hence, the required value of x is $6°$ .