Question

algebra for exercises 20 - 22, use the figure at the right. 20. if (mangle cfd=12a + 45), find (a) so that (overrightarrow{fc}perpoverrightarrow{fd}).

Explanation:

Step1: Recall perpendicular - angle property

If $\overrightarrow{FC}\perp\overrightarrow{FD}$, then $m\angle CFD = 90^{\circ}$.

Step2: Set up the equation

Set $12a + 45=90$.

Step3: Solve for $a$

Subtract 45 from both sides: $12a=90 - 45$, so $12a = 45$. Then divide both sides by 12: $a=\frac{45}{12}=\frac{15}{4}=3.75$.

Answer:

$a = 3.75$