Question

In SABC, 2B-90", D is point on side AC such that BD is perpendicular to AC. If BD - 8 cm and
AD 4 cm, find the value of AC.​

Answer 1

Answer:

AC =

$4 \sqrt{5}$

Step-by-step explanation:

Given that, 2B = 90°

So, B = 45°

In Triangle ABC, A + B + C = 180° [ASP]

90° + 45° + C = 180°

So, C = 180° - 135°

C = 45°

As, B = C = 45°

As, Opp. Angles are Equal so the sides facing them will also be equal

So, AB = AC - - - - - - (1)

In Triangle ADB [Angle D = 90°]

${h}^{2} = {p}^{2} + {b}^{2}$

So,

${ab}^{2} = {bd}^{2} + {ad}^{2} \\ {ab}^{2} = \ {8}^{2} + {4}^{2} \\ {ab}^{2} = 64 + 16 \\ {ab}^{2} = 80 \\ ab = \sqrt{80} \\ ab = 4 \sqrt{5}$

As, AB = AC - - - - - [From (1)]

So, AC =

$4 \sqrt{5}$