Question

Given: ABC is a right triangle with right angle C. ​ AB=14 centimeters ​ and m∠A=33∘ .

What is AC ?

Answer 1

check the picture below.

make sure your calculator is in Degree mode.

Answer 2

AC = 11.74 cm.

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,

`cos A= (Adjacent \ side)/(Hypotenuse)`

Plugging values of adjacent side and Hypotenuse and <A in above formula, we get

cos 33° =
`(AC)/(AB)`

cos 33° =
`(AC)/(14)`

Plugging cos 33° = 0.83867, we get

0.83867=
`(AC)/(14)`

On cross multiplying both sides by 14, we get

0.83867×14=
`14 * (AC)/(14)`

11.74 = AC.

Therefore, AC = 11.74 cm.