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In the right △ABC with m∠C = 90°, m∠A = 75°, and AB = 12 cm. Find the area of △ABC.

User Seann
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2 Answers

6 votes
The Answer is 18, the steps are in the picture
In the right △ABC with m∠C = 90°, m∠A = 75°, and AB = 12 cm. Find the area of △ABC-example-1
User Bwoogie
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4 votes

Answer:

The area of △ABC is
18 cm^2

Explanation:

We are given a right triangle △ABC, with m∠C = 90°, m∠A = 75°, and AB = 12 cm. If we graph all the triangle data, we can see that we have the length of the hypotenuse, and one of the angles.

Using the trigonometric functions sine, cosine and tangent (Remember SOH CAH TOA), we can calculate the triangle legs, in the following form:


\overline{AC}=(12cm)*cos(75)=(3\sqrt6+3\sqrt2)cm\approx3.10cm

for the leg
\overline{AC}, and


\overline{BC}=(12cm)*sin(75)=(3\sqrt6+3\sqrt2)cm\approx11.59cm

for the leg
\overline{BC}.

Finally, to know the area, we just use the area of a triangle formula:


area (\triangle ABC)=\frac{\overline{AC}*\overline{BC}}{2}=((3\sqrt6+3\sqrt2)(3\sqrt6+3\sqrt2))/(2)cm^2=18cm^2

User Dagoof
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