Question

In the figure, if CD = 15 cm, then BC ≈ cm.

Answer 1

Answer-

$\boxed{\boxed{BC=21.5\ cm}}$

Solution-

Triangle ABC and ABD are right angle triangle.

From trigonometric properties,

$\tan \theta=\dfrac{Perpendicular}{Base}$

In Triangle ABC

$\tan 40=\dfrac{AB}{BC}=\dfrac{AB}{BD+CD}\\\\\Rightarrow AB=\tan 40\cdot (BD+CD)$

In Triangle ABD

$\tan 70=\dfrac{AB}{BD}\\\\\Rightarrow AB=\tan 70\cdot (BD)$

From the above two equations,

$\Rightarrow \tan 40\cdot (BD+CD)=\tan 70\cdot (BD)$

$\Rightarrow \tan 40\cdot (BD+15)=\tan 70\cdot (BD)$

$\Rightarrow BD+15=\dfrac{\tan 70}{\tan 40}\cdot (BD)$

$\Rightarrow BD+15=3.3BD$

$\Rightarrow 3.3BD- BD=15$

$\Rightarrow 2.3BD=15$

$\Rightarrow BD=\dfrac{15}{2.3}=6.5\ cm$

Therefore, $BC=BD+CD=6.5+15=21.5\ cm$

Answer 2

Answer:

21.6 is the only option.

Step-by-step explanation: