Question

In abc above,what is the length of ad​

Answer 1

Answer:

B

Step-by-step explanation:

First calculate BD using sine ratio in Δ BCD and the exact value

sin60° = $\frac{\sqrt{3} }{2}$, thus

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{BD}{BC}$ = $\frac{BD}{12}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2BD = 12$\sqrt{3}$ ( divide both sides by 2 )

BD = 6$\sqrt{3}$

-----------------------------------------------------------

Calculate AD using the tangent ratio in Δ ABD and the exact value

tan30° = $\frac{1}{\sqrt{3} }$ , thus

tan30° = $\frac{opposite}{adjacent}$ = $\frac{AD}{BD}$ = $\frac{AD}{6\sqrt{3} }$ = $\frac{1}{\sqrt{3} }$ ( cross- multiply )

$\sqrt{3}$ AD = 6$\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

AD = 6 → B