Question

2) In the adj. fig. seg AD 1 side BC ZC = 45°, AC = 8V2 cm, BD = 5cm. Find AD.​

Answer 1

Given that :- In Δ$ABC$,

$AD$⊥$BC$, ∠$C=45^{o}$

$BD = 5 cm$

$CD=8cm$

$AC = 8\sqrt{2}$

As we have to find the value of AD,

So, $BC=BD+DC$

⇒ $BC=5+8$

⇒ $BC=13cm$

Now for AD,

By using pythagoras theorem,

⇒ $a^{2}=(6)^{2} +c^{2}$

⇒ $(AC)^{2} =(AD)^{2} +(DC)^{2}$

⇒ $(8\sqrt{2} )^{2} =(AD)^{2} +(DC)^{2}$

⇒ $128=(AD)^{2} +(8)^{2}$

⇒  $(AD)^{2} =128-64$

⇒  $(AD)^{2} =64$

⇒  $AD = \sqrt{64}$

⇒ $AD=8 units$

Thus, the required value of $AD$ is $8 units$