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Ksivusya [100]
3 years ago
7

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

Mathematics
2 answers:
FrozenT [24]3 years ago
6 0
Check the picture below.

make sure your calculator is in Degree mode.

dmitriy555 [2]3 years ago
3 0

Answer:

<h3> AC = 11.74 cm.</h3>

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,

cos A= \frac{Adjacent \ side}{Hypotenuse}

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

cos 33° = \frac{AC}{AB}

cos 33° = \frac{AC}{14}

Plugging cos 33° = 0.83867, we get

0.83867= \frac{AC}{14}

On cross multiplying both sides by 14, we get

0.83867×14= 14 \times \frac{AC}{14}

11.74 = AC.

<h3>Therefore, AC = 11.74 cm.</h3>
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Given that after triangle ACE is dilated by a factor of 6, it has an area of 180 square inches.

Thus, it means the dilated area is 6 times the area before dilation.

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