Question

∆ABC angle A= 90° angleC=30° AC=27cm AB =?​

Answer 1

ΔABC is right angled at B, so AC is the hypotenuse.

AC−AB=1       ...Given     ....(1)

By Pythagoras theorem,

AC2=AB2+BC2

BC2=AC2−AB2

72=(AC−AB)(AC+AB)

49=1(AC+AB)

So, AC+AB=49     ....(2)

Adding (1) and (2) we get,

⇒2AC=50

⇒AC=25 

Sbstitute in eq (2), we get

AB=24 cm.

Now, cosA+sinA= AB/AC+BC/AC 24/25+7/25=31/25

⇒cos A+ Sin A = 31/25