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 $AB = 20$ and $A = 49^{\circ}$, then $BC=AB\sin A$. So, $BC = 20\times\sin49^{\circ}$. Using a calculator, $\sin49^{\circ}\approx0.7547$, and $BC = 20\times0.7547 = 15.094$.

Step2: Find length of BD in right - triangle BCD

In right - triangle BCD, $\sin D=\frac{BC}{BD}$. We know $BC = 15.094$ and $D = 26^{\circ}$, so $BD=\frac{BC}{\sin D}$. Since $\sin26^{\circ}\approx0.4384$, then $BD=\frac{15.094}{0.4384}\approx34.43$.

Answer:

$34.43$