I've been trying to brush up on my trigonometry, but I have realised that I need some help. I'm in the process of building a table, where the legs are connected to the table at a 6 degree angle in both the x and y axis if looking from the bottom of the table.
The dimensions of the table is fixed at (1) long edge = 150 cm, (2) short edge = 60 cm, (3) hight of table should be = 45 cm
I have three main questions. (1) How far from the table edges should the drill hole be, for the end of the table leg (the part hitting the floor) to be perpendicular(?) to the table edge. (2) how long do the table leg need to be, to get a table hight of 45 cm when angled at 6 degrees (3) If the table leg is angled 6 degrees towards the short and and the long end. What is the angle towards the corner of the table?
I've tried below. But I think Im doing something, wrong as the results dont make sense… Hope you guys can spot my errors.
Best Answer
Hint: What you have is a square pyramid with square length $a$ and height $45\,$cm with its apex perpendicularly above one of the squares vertex. Thus, two of the pyramids sides are right triangles with legs $45\,$cm and $a$, one of the angles being $6^{\circ}$, thus use tangens to calculate $a$. Finally, to get the length of the table leg, consider right triangle with one leg being the diagonal of the square (thus, having length $a\sqrt 2$) and the other being the height of the pyramid (thus, having length $45\,$cm). Hypotenuse of that triangle is table leg. Now use whatever trigonometric function you want to calculate the angle you want.
Alternatively, think of right square prism with square sides having length $a$ and its height $45\,$cm. Calculations are as described above.