Quote (PiXi31415 @ Dec 17 2022 10:00am)

according to the picture:
the full triangle is not rectangular, so we have to divide it into rectangular triangles, if we want to use simple trigonometrics. this is easily achievable by just cutting it in the middle, like it is drawn in the picture (reason for that is that the triangle is symmetric). naming half (!) of the bottom side 'd', we can apply the definition of the cosine:
cos(30 deg) = d/4m, so d = 4m*cos(30 deg) = 3.4641 m
now we can get the full length of the beam by just doubling this number: 2d = 6.9282 m

Quote (RollOneUp @ Dec 17 2022 04:28pm)

which formula would i use to do it this way? that’s as throwing me off also the line down the middle , if you could lay out all the work you did and which formula so i can plug it all in, that would be helpful !

Quote (PiXi31415 @ Dec 17 2022 10:49am)

first of all, you have to realize that sine/cosine/tangent are defined as ratios of sides in a right triangle. this means (and it is very important!) that you have to divide your geometric problem into right triangles to use the according formulas for sin/cos/tan. the picture you have posted shows a triangle with angles 30, 30 and 120 deg (the large angle was calculated correctly in one of your posts above since the sum of all angles in a triangle is 180 deg and 180-30-30 = 120). thus, there is no right angle in the given triangle and sin/cos/tan cant be used right away. to get right triangles, we have to split it: draw a line from the top corner down to the bottom side, that is perpendicular to the bottom side. this divides the big triangle into two small ones, that now have a right angle (marked by the small square in your picture)! now we can apply sin/cos/tan:
consider the small triangle on the right. the angle in the bottom corner is given as 30 deg. the side opposite to the right angle (i.e. the hypotenuse) is given to have a length of 4 m. the side that we want to calculate is the adjacent side of the 30-deg-angle. this means, you should use the cosine: cos(30 deg) = adj/hyp. solve for the adjacent: adj = hyp*cos(30 deg) = 4 m *cos(30deg) = 3.4641
alternatively, you could have achieved this in another way: the angle in the top of the small triangle has to be (tel:180-90-30180-90-30[/URL]) deg = 60 deg. with respect to this angle, the side to be calulated is the opposite. calculating the sine leads to: sine(60 deg)= opp/hyp, rearranging leads to opp = hyp*sin(60 deg) = 3.4641 as well
remember, this is the bottom side of the right triangle only! to calculate the total length of the bottom side, you have to either do all that for the left small triangle as well or consider that the big triangle is symmetric and just double the number calculated earlier