Answer:
AC = 11.74 cm.
Step-by-step explanation:
Given right triangle ABC with right angle at C.
Also side AB = 14 centimeters and
m∠A=33° .
We need to find the length of side AC.
Because < C is right angle, therefore side AB would be Hypotenuse (longest side) of the right triangle.
And side AC would become adjacent side of angle <A.
So, in order to find the side length AC, we can apply cosine ratio.
We know,
[tex]cos A= \frac{Adjacent \ side}{Hypotenuse}[/tex]
Plugging values of adjacent side and Hypotenuse and <A in above formula, we get
cos 33° = [tex]\frac{AC}{AB}[/tex]
cos 33° = [tex]\frac{AC}{14}[/tex]
Plugging cos 33° = 0.83867, we get
0.83867= [tex]\frac{AC}{14}[/tex]
On cross multiplying both sides by 14, we get
0.83867×14= [tex]14 \times \frac{AC}{14}[/tex]
11.74 = AC.
Therefore, AC = 11.74 cm.
