Question

In the given figure angle angle ABC =90 degree AC = 13 CD =11 AD=20. Find BC and AB​

Answer 1

Step-by-step explanation:

Let BD=x cm.

∠ADB = ∠CDB = 90∘ . That is, ΔADB and ΔCDB are right-angled triangles, with AD=9 cm and BD=4 cm.

Consider ΔADB right-angled at D .

tanA=BDAD=x9…(1)

Similarly, in ΔCDB right-angled at D ,

tanC=BDCD=x4…(2)

It is given that ΔABC is a right-angled triangle, right-angled at B .

∴A+C=90∘,C=90∘−A,tanC=tan(90∘−A)=cotA=1tanA

Substituting for tanA and tanC from (1) and (2), we obtain

x4=9x,x2=36

Therefore the length of segment BD=x=6 cm.