Hinges can work, I have used this technique before, if you sandwich the hinges between two plates you get 45 degree 'bricks' that are quite solid.
In most cases, tiles and plates in the right place will keep sufficient contact with the base plate to have a stable model.
45° angles are tricky because of the dimensions of 45-45-90 triangles:
The fact that the hypotenuse needs to be a multiple of radical two makes it difficult to build out of LEGO plates which are generally limited to integers or halves. The best you can do in a reasonably small amount of space is a 5 x 5 x 7.07 triangle, but that doesn't come close enough to ...
Scale is the obvious answer. The Legoland model is huge, which means you're not seeing the brick-level quantisation as easily (quantisation is most obviously seen in mosaics but that works in 3D too).
Getting the same effect at smaller scales usually means a lot of SNOT and using sloped bricks. These days there is a huge range of slopes available, from 4 ...
It appears that some LEGO pieces are designed with the proportions of 45-degree right triangles in mind. For example, the 3x3 plate with one corner removed has a diagonal edge that is very close to three studs long, as can be seen in this construction:
Likewise, the 8x8 corner plate has a diagonal edge that is very close to 10 studs long:
You are trying to assemble a triangle with inclined parts of 8 units in length and horizontal line is 7 units. The rest is math:
∠α = cos⁻¹(3,5÷8) = 64.0555°
Due to slight imperfection in LEGO assembly you can easily take a value of 64° for one side and 296° (you were close!) for another.
I did a mock-up in LDCad and proved that it works with angle of 64°, ...
There are many different types. You can find them here: Bricklink - Brick Modified
There are also Brackets: Bricklink - Brackets
And you could use some of these Bricklink - Plate Modified or, of course, these Bricklink - Hinges
There are many. I believe the classic "Erling"/headlight brick (it was designed by a guy named Erling) is the oldest way, but there's also a number of bricks with studs on the side and a number of brackets.
To get the exact answer, this is what high school geometry and trig is useful for in the real world :)
Alternatively, switch off collision detection and just try changing the angles in small increments (e.g. 1 degree) until it looks right. Type the angle into the box shown in the picture, don't try to rotate the parts with the mouse.
Then switch collision ...
A 45 degree slope doesn't fit the standard geometry of the LEGO system.
The basic "3D module" of the system (a 1x1 plate) is 5 units square by 2 units tall.
A brick is three plates tall - i.e. 5 units square by 6 units tall.
Therefore, the smallest perfect cube you can build is 6 bricks square by 5 bricks tall. It should be clear that can't be ...
Since no one has answered this, I'll reproduce my comment as an answer:
If you are just going for something aesthetically close, and not load bearing, why do you need the hinge piece on the top? Just push the long hinge plate up in to the "awning" and then your problems are solved.
A straight forward wall of Lego bricks will have some pliability that can be used to a Master Builder's advantage. I did manage to find a YouTube video that sums it up nicely.
Yeah you pretty much have the two choices you outlined... hinges or make it so big that the squareness of the bricks melts into nothingness at that resolution.
OR... build your structure over tiles and use single studs, like at the ends of the ends of the hypotenuse of a 3-4-5 triangle... but that will be seriously flimsy the higher you build the walls, ...