Question

33. DF bisects ZEDG. Find the value of x. The diagram is not to scale.

Answer 1

From the given diagram, we can identify two right-angled triangles. The triangles are shown below:

Using trigonometric ratios, we can find x as follows

$\begin{gathered} \sin 28^0\text{ = }\frac{7x\text{ + 15}}{DF} \\ \sin 28^0\text{ = }\frac{10x}{DF} \end{gathered}$

We can equate the expressions for DF as follows:

$\begin{gathered} DF\text{ = }\frac{7x\text{ + 15}}{\sin 28^0} \\ DF\text{ = }\frac{10x}{\sin 28^0} \end{gathered}$$\begin{gathered} \frac{7x\text{ + 15}}{\sin28^0}\text{ = }\frac{10x}{\sin 28^0} \\ \text{Cancelling out sin 28}^0 \\ 7x\text{ + 15 = 10x} \end{gathered}$

Solving for x:

$\begin{gathered} 7x\text{ - 10x = -15} \\ -3x\text{ = -15} \\ \text{Divide both sides by -3} \\ \frac{-3x}{-3}\text{ = }\frac{-15}{-3} \\ x\text{ = 5} \end{gathered}$

Answer:

x = 5