Question

1. what is the length of the altitude, segment cd, of triangle abc?

a. $6\sqrt{3}$ square units
b. $12\sqrt{3}$ square units
c. $12\sqrt{2}$ square units
d. $6\sqrt{2}$ square units

Explanation:

Step1: Identify right triangle CBD

In $\triangle CBD$, $\angle B = 60^\circ$, $\angle CDB = 90^\circ$, $BC=12$.

Step2: Use sine for altitude $CD$

$\sin(60^\circ)=\frac{CD}{BC}$
$CD = BC \times \sin(60^\circ) = 12 \times \frac{\sqrt{3}}{2}$

Step3: Calculate final value

$CD = 6\sqrt{3}$

Answer:

a. $6\sqrt{3}$ square units