What is side AC? for the diagram below

Question

asked Jul 27, 2024 94.5k views

1 Answer

ShuklaSannidhya · Answer 1 · 2024-08-02T01:00:40+0000

Length of side AC = 12√2

From the given diagram,

$\sf \angle C$ = 30°

Also, AB = base

AC = Hypotenuse

BC = perpendicular

Using trigonometric ratio,

$\Rightarrow \sf (Base)/(Hyp.) = sin \theta$

Plugging the required values, have

$\Rightarrow \sf \frac {AB}{AC} = sin 30\degree \\$

$\Rightarrow \sf (6 √(2) )/(AC) = (1)/(2) \: \: \: \: \: \bigg( \because \sin30 \degree = (1)/(2) \bigg ) \\$

Further solving by cross multiplication,

$\Rightarrow \sf AC = 2 * 6 {√(√2 )}$

$\Rightarrow \sf AC = {12√(2)}$

Henceforth Length of side AC is 12√2