Question

find bd.

write your answer as an integer or as a decimal rounded to the nearest tenth.
bd =
submit
work it out

Explanation:

Step1: Identify trigonometric ratio

In right $\triangle BCD$, $\angle C=40^\circ$, $BC=6$, $BD$ is opposite $\angle C$, $BC$ is adjacent to $\angle C$. Use tangent:
$\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(40^\circ)=\frac{BD}{6}$

Step3: Solve for BD

$BD=6\times\tan(40^\circ)$
Calculate $\tan(40^\circ)\approx0.8391$, so:
$BD\approx6\times0.8391=5.0346$

Step4: Round to nearest tenth

$BD\approx5.0$

Answer:

$5.0$