So over there is a best triangle $ABC$ with $m∠C=90°$, $m∠B=75°$, and $BC\ (the \ hypotenuse)=12 cm$. I desire to uncover the area of this triangle

It would look something like this:

Note: ns have already solved this problem and also got the answer together $18$ $cm^2$. So, i am not searching for an answer, i am in search of another way to deal with this problem.

You are watching: 15-75-90 triangle

Ex. Https://centregalilee.com/a/2082666/521593

If anyone can help, discover this way it would certainly be most appreciated. Thanks.

geometry trigonometry triangle
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edited Sep 23 "18 at 2:33

DeepSea
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asked Sep 23 "18 at 2:29

Atrey DesaiAtrey Desai
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Here is her triangle with just one extra segment inscribed in it:

Now you have actually a $30$-$60$-$90$ triangle, whose ratios friend presumably know.That is, you know the ratios the $AC$ and also $AD$ come $CD.$But likewise $BD=CD$ and also $AB = ad + BD,$ for this reason you have actually the ratio $AB : CD,$and currently you have the right to use the Pythagorean theorem to acquire the proportion $BC: CD.$But $BC = 12,$ and using the ratios friend have uncovered you deserve to assign lengths to every the various other segments, in details $AB$ and also $AC.$Then you can find the area.

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answered Sep 23 "18 at 3:21

David KDavid K
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We deserve to use the chords nature of a Dodecagon:

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answered Sep 24 "18 in ~ 0:27

SeyedSeyed
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Draw a perpendicular native A come the hypotenuse

Now find length that perpendicular using an easy trignometry and Area that Triangle = $1\over2(BC)(Lenght\ of\ perpendicular)$

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edited Jun 12 "20 at 10:38

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answer Sep 23 "18 at 2:40
AwakenedAwakened
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