Maths geometry question??

[Perik Omo]

For the life of me I can't remember the formula for this, haven't been to school since 1963!! I have a shape that can be describes as an irregular rectangle for which I have all 4 angles and 3 sides and I need to calculate the length of the 4th side.

angle a = 90
angle b = 90
angle c = 80 (slope of 10 degrees is needed)
angle d = 170
height (angle a to angle c) = 266
height (angle c to angle d) = 200
base length = 395
length of top (angle c to angle d) = ?

Is this a quadrilateral with two right angles or an irregular rectangle? I thought quadrilaterals had 4 unequal angles.

OK, over to the mathematicans out there....

Edited by Perik Omo on Sunday 11th September 12:13

[lufbramatt]

Make it into 2 triangles ( or a rectangle and a triangle, can't quite visualise the shape) then use sin/cos/tan to find the missing side. A picture would help :-)

[Chester draws]

Need a picture.

Are you sure on the 170° and 10°?

I guess 400.476.

[Collectingbrass]

Perik Omo said:

For the life of me I can't remember the formula for this, haven't been to school since 1963!! I have a shape that can be describes as an irregular rectangle for which I have all 4 angles and 3 sides and I need to calculate the length of the 4th side.

angle a = 90
angle b = 90
angle c = 10
angle d = 170
height (angle a to angle c) = 266
height (angle c to angle d) = 200
base length = 395
length of top (angle c to angle d) = ?

Is this a quadrilateral with two right angles or an irregular rectangle? I thought quadrilaterals had 4 unequal angles.

OK, over to the mathematicans out there....

To be honest I’d draw it to scale and measure the missing side…

I’m not sure I understand your shape from your description. I think you’re saying:
Side AC = 266 units
Side CD = 200 units – CD is also the length we need to find as I read it, so is this meant to be side BD? This would make sense is the base is side AB?
Base = 395 units. Is this side AB?

Angles: Side AC to AB = a = 90
AB to BD = b = 90
AC to CD = c = 10
BD to CD = d = 170

Is this right?

[Perik Omo]

Chester draws said:

Need a picture.

Are you sure on the 170° and 10°?

I guess 400.476.

No, I just came back in to correct that. The internal angle at that corner is 80 degrees, not 10 degrees (a slope of 10 degrees is needed)!!

[Doofus]

In which case, angle D isn't 170. The internal angles need to add up to 360. So 90+90+80=260, and angle D is therefore 100.

Anyway; make a triangle out of the top of the shape. You know one vertical is 266, and the other is 200. So you have a triangle of base 395m vertical 66.

Therefore 395^2 + 66^2 = hyp^2.

156,025 + 4,356 = 160,381. sqrt 160,381 = 400.48, which is what somebody else has already said.

[Perik Omo]

Collectingbrass said:

Perik Omo said:

For the life of me I can't remember the formula for this, haven't been to school since 1963!! I have a shape that can be describes as an irregular rectangle for which I have all 4 angles and 3 sides and I need to calculate the length of the 4th side.

angle a = 90
angle b = 90
angle c = 10
angle d = 170
height (angle a to angle c) = 266
height (angle c to angle d) = 200
base length = 395
length of top (angle c to angle d) = ?

Is this a quadrilateral with two right angles or an irregular rectangle? I thought quadrilaterals had 4 unequal angles.

OK, over to the mathematicans out there....

To be honest I’d draw it to scale and measure the missing side…

I’m not sure I understand your shape from your description. I think you’re saying:
Side AC = 266 units
Side CD = 200 units – CD is also the length we need to find as I read it, so is this meant to be side BD? This would make sense is the base is side AB?
Base = 395 units. Is this side AB?

Angles: Side AC to AB = a = 90
AB to BD = b = 90
AC to CD = c = 10
BD to CD = d = 170

Is this right?

OK, I'm playing with the design of a car port and the only fixed things are the height of 266cm against the wall, the slope of 10 degrees from the wall and, at the moment, the distance from the wall to the support post is 395cm.

So, the wall is A B, the distance to the post is A C and the distance from the top of the post back to the wall is D C (which is what I need to find for the length of the rafters). Angle (a) is the angle against the wall, angle (b) is the base against the post, angle (c) is the top corner of the post back to the wall and angle (d) is the wall back to the post (sorry that's 80 degrees giving a slope od 10 degrees).

[Planet Claire]

It sounds like you are describing a trapezium, but I can't quite work out which side you are trying to work out - is it the 'sloping' side? If so then you'll have to split the shape up into a rectangle and right-angled triangle and then use the triangle and Pythagoras to work out the length of the hypotenuse (the sloping side).

Pythagoras says that the square on the hypotenuse is equal to the sum of the squares on the other two sides. For a right-angled triangle of sides a, b and c, where c is the hypotenuse, then a^2+b^2=c^2.

Hope that helps.

[Perik Omo]

OK thanks all, I realise now that the 170 degree angle was wrong and should be 100 degrees which confused things somewhat. I'e been using the two triangle method and subtracting the hypotenuse length of the smaller to get the length of the slope of the larger.

[Collectingbrass]

The height of the wall doesn't matter, the rafter length is the length of the horizontal span divided by the cosine of the angle of the pitch of the roof. In your case 4.010m.

HOWEVER, you don't need a roof fall of ten degrees. The minimum you need is a pitch of 1:40, or 1 up for every 40 in width. Which makes the rafters near as dammit 3.950m

NB these are the clear span lengths and you need to allow for whatever is supporting the rafters at each end, plus some for triming and gutter support and buggeration. Have a look here http://www.diydoctor.org.uk/projects/building_a_fl...

Where does the height of 2.66m come from? If it's for a car porch you need a clear height of minimum 2.1m to stand upright, then some for for the rafter depth & roof construction.

Edited by Collectingbrass on Sunday 11th September 12:52

[Mr Pointy]

[xRIEx]

Perik Omo said:

Is this a quadrilateral with two right angles or an irregular rectangle? I thought quadrilaterals had 4 unequal angles.

A quadrilateral is any polygon with for sides. Rectangles, squares, trapeziums, parallelograms and rhombuses are all quadrilaterals.

A rectangle is a quadrilateral with 4 right angles (which includes squares).

Any polygon described as 'regular' has equal angles and sides, so a square is a regular rectangle.

So in this long-winded way of answering your question, it's a quadrilateral with two right angles.

[battered]

An easier way of addressing your question is to see it as a rectangle with a triangle on top. Draw a horizontal line at 2m, there you go. All your schoolboy maths now works with ease. It's a right angle triangle on a box. Or in 3D a wedge of cheese on a box.

[Perik Omo]

Whew, thanks all. I can do it now.