Question

Solve the triangle for x.

Answer 1

For this case we have that the law of cosine is given by:

`c ^ 2 = a ^ 2 + b ^ 2-2 (a) (b) * cos (x)`

Where:

`c = 12 \ ft\\a = 8 \ ft\\b = 9 \ ft`

We replace:

`12 ^ 2 = 8 ^ 2 + 9 ^ 2-2 (8) (9) * cos (x)\\144 = 64 + 81-144 * cos (x)\\144 = 145-144 * cos (x)\\-1 = -144cos (x)\\cos (x) = \frac {1} {144}\\x = cos ^ {- 1} (\frac {1} {144})\\x = 89.60 \ degrees`

Answer:

Option B