Question

Find the value of x.

Round to the nearest tenth.
х
16
30°
30
x = [?]
need help asap:(

Answer 1

`x\approx 18.0`

Explanation:

Here, a = 30, b = 16, C = x

By law of cosines

`{c}^(2) = {a}^(2) + {b}^(2) - 2ab \cos C \\ \\ {x}^(2) = {30}^(2) + {16}^(2) - 2 * 30 * 16 \: cos 30 \degree \\ \\ {x}^(2) = 900 + 256 - 960 * ( √(3) )/(2) \\ \\ {x}^(2) = 1156 - 480 * √(3) \\ \\ {x}^(2) = 324.615612 \\ \\ x = √(324.615612) \\ \\ x = 18.0170922 \\ \\ x \approx \: 18.0`