Find angles and area of this trapezoid: 4 side lengths, 1 angle measure known

Richacinas

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Apr 25, 2018
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Hello there!

I'm new to this forum.

I'm trying to find the angles and area of this shape:

WhatsApp Image 2018-04-25 at 11.27.29.jpg

The angle on the right bottom corner, is square (90deg).

I'm wondering if there is a way to find the other angles and area of this shape.


Thanks a lot in advance for your help :D
 
I'm trying to find the angles and area of this shape:

View attachment 9412

The angle on the right bottom corner, is square (90deg).

I'm wondering if there is a way to find the other angles and area of this shape.

One way is to find the length of the diagonal from lower left to upper right; and use simple trig to find the angles in that right triangle. Then you will know all sides of the remaining triangle (upper left), and can use the Law of Cosines to find its angles.

For the area, the right triangle is easy, and you can use Heron's (Hero's) formula for the area of the other triangle.

If you tell us your context, including how much trig you know and how far you can get in carrying this out, we can help you further.
 
One way is to find the length of the diagonal from lower left to upper right; and use simple trig to find the angles in that right triangle. Then you will know all sides of the remaining triangle (upper left), and can use the Law of Cosines to find its angles.

For the area, the right triangle is easy, and you can use Heron's (Hero's) formula for the area of the other triangle.

If you tell us your context, including how much trig you know and how far you can get in carrying this out, we can help you further.

Ahhh, you are right! I know enough trigonometry as to know what you are talking about hehehe. Really your help was more than enough and all I need is to find that diagonal.

I took a lot of maths during school and my computer science degree, but the knowledge was buried somewhere..

Thanks so much
 
Ahhh, you are right! I know enough trigonometry as to know what you are talking about hehehe. Really your help was more than enough and all I need is to find that diagonal.

I took a lot of maths during school and my computer science degree, but the knowledge was buried somewhere..

Thanks so much

Great! It's nice when just a suggestion is all you need.
 
Last edited:
Curious: why did you write "Plato" inside your quadrilateral?
Haha! It is a shower cabin, I had to order a special shape for my bathroom so I wanted to do all the math and make sure that they do it right at the factory.

In Spanish, the bottom area where you stand and that can be made of minerals or ceramic, is called "Plato de ducha".

I tried to attach a picture of the result. Thanks a lot guys,

Ricardo
 

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