Answer:
The length of CD is:
Option: B 5.9 m
Step-by-step explanation:
We need to use the trigonometric ratio in order to find the value of the length of CD.
In right angled triangle CBA we have:
[tex]\tan 28\°=\dfrac{CB}{AB}\\\\i.e.\\\\0.53171=\dfrac{CB}{85}\\\\i.e.\\\\CB=45.195[/tex]
Also, in right angled triangle i.e. ΔABD we have:
[tex]\tan 31\°=\dfrac{BD}{AB}\\\\i.e.\\\\\tan 31\°=\dfrac{CB+CD}{85}\\\\i.e.\\\\CB+CD=\tan 31\°\times 85\\\\i.e.\\\\CB+CD=51.0732\\\\i.e.\\\\CD=51.0732-CB\\\\i.e.\\\\CD=51.0732-45.195\\\\i.e.\\\\CD=5.8782[/tex]
which to the nearest tenth is:
[tex]CD=5.9\ m[/tex]
Hence, option: B is the correct answer.
