Question

calculate the value of bd correct to 2 decimal places.

Explanation:

Step1: Find length of BC in right - triangle ABC

In right - triangle ABC, $\sin A=\frac{BC}{AB}$. Given $AB = 8$ and $A = 20^{\circ}$, then $BC=AB\sin A=8\times\sin(20^{\circ})$.
$BC = 8\times0.3420\approx2.74$.

Step2: Find length of BD in right - triangle BCD

In right - triangle BCD, $\sin D=\frac{BC}{BD}$. Given $D = 18^{\circ}$ and $BC\approx2.74$, then $BD=\frac{BC}{\sin D}$.
$BD=\frac{2.74}{\sin(18^{\circ})}=\frac{2.74}{0.3090}\approx8.87$.

Answer:

$8.87$