Well...I wanted to be consistent with the definitions recommended here https://en.wikipedia.org/wiki/Gigabyte
I just really hope that in the future we can all agree on the same prefixes to mean the same things.
I have never heard of Appollonius's Theorem, but does seem like it can be used here.
Using the information from here: https://en.wikipedia.org/wiki/Apollonius%27s_theorem
32 + 42 = 2( (2a)2 + a2 ) | |
25 = 2( 4a2 + a2 ) |
|
25 = 2( 5a2 ) | |
25 = 10a2 |
|
2.5 = a2 | |
a = √[ 2.5 ] |
|
BC = 2a = 2√[ 2.5 ] |
By the Law of Sines:
sinB10=sin(π6)6 sinB=10sin(π6)6 sinB=56 B≈56.44°orB≈123.56°
Both options are valid in this case because neither make the current sum of the angles exceed 180° .
Using the first possible value of B, that is, B = arcsin(5/6)
| Using the second possible value of B, that is, B = π - arcsin(5/6)
|
A=π−B−C A=π−arcsin(56)−π6 A=5π6−arcsin(56) sin(A)=sin(5π6−arcsin(56)) sin(A)=(12)(√116)−(−√32)(56) sin(A)=√11+5√312
By the Law of Sines:
sinABC=sinπ66 sinABC=112 BCsinA=121 BC=12sinA BC=12(5√3+√1112) BC=5√3+√11 | A=π−B−C A=π−(π−arcsin(56))−π6 A=arcsin(56)−π6 sin(A)=sin(arcsin(56)−π6) sin(A)=(56)(√32)−(√116)(12) sin(A)=5√3−√1112
By the Law of Sines:
sinABC=sinπ66 sinABC=112 BCsinA=121 BC=12sinA BC=12(5√3−√1112) BC=5√3−√11 |
the first possible value of BC + the second possible value of BC = (5√3+√11)+(5√3−√11)
the first possible value of BC + the second possible value of BC = 10√3
.