Question

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

Answer 1

21.6 is the only option.

Explanation:

Answer 2

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

Solution-

Triangle ABC and ABD are right angle triangle.

From trigonometric properties,

`\tan \theta=(Perpendicular)/(Base)`

In Triangle ABC

`\tan 40=(AB)/(BC)=(AB)/(BD+CD)\\\\\Rightarrow AB=\tan 40\cdot (BD+CD)`

In Triangle ABD

`\tan 70=(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=(\tan 70)/(\tan 40)\cdot (BD)`

`\Rightarrow BD+15=3.3BD`

`\Rightarrow 3.3BD- BD=15`

`\Rightarrow 2.3BD=15`

`\Rightarrow BD=(15)/(2.3)=6.5\ cm`

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