Find FM using Pythagoras Theorem:
We're not after c^2 using pythag - rearrange it:
It don't matter were the B or A is in the equation - it'll give u the missing length you're after.
c^2 - b^2 = a^2
8^2 - 5^2 = a^2
Square root both sides to get A on its own
A= root 8^2 - 5^2
= root 39
= 6.24499....
Or
6.24cm, but FM is root 39 I'll use throughout, even if I use 6.24 in calculations, it's to make things clearer for you.
Create diagonal line from B to E - drawing right-angle triangle A to B to E back to A.
AB is 16cm
AE is 8cm - given above
(because the triangle at the front & back are the same.)
Use Pythagoras Theorem for length BE:
a^2 + b^2 = c^2
16^2 + 8^2 = c^2
Square root
C = root 16^2 + 8^2
= 8 root 5
= 17.8885...
8 Square root 5 - I'll use for BE
Creat another triangle to find the angel -
B to E to (M between the length AD)
However, diagonal line B to M needed.
So, m is the mid-point of the base triangle, pretend to slice it in half from point M - this creates a mini rectangle. (ABM to MA - with M on side AD)
Now use this to find B to M:
(if MC is 5cm, BM is 5cm - on length BC)
C = root 16^2 + 5^2
= root 281
= 16.76305...
= 16.76
Create right-angle triangle:
Be to M back to B
BE= 8 root 5
EM = root 39
MB = root 281
So, the angle will be from EB to M.
EB is the hypotenuse
BM is the adjacent
AH means Cah, but the inverse
Cos-1(a/h)
Cos-1(root 281 / 8 root5) = 20.4326...
Thus, angle we're after is 20.43 degrees to 2.dp
(The easiest way for me to explain - it took a while)
Hope this helps!
