Question

Calculate the length b to two decimal places.

Answer 1

B. 21.64

Step-by-step explanation:

We have been given a triangle and we are asked to find the length of AC (b).

We will use law of cosines to find the length of side AC.

`c^(2)=a^(2)+b^(2)-2ab \text{ cos }\theta`

Upon substituting our given values in the formula we will get,

`(AC)^(2)=15^(2)+12^(2)-2* 15* 12 \text{ cos}(106)`

`(AC)^(2)=225+144-360\text{ cos}(106)`

`(AC)^(2)=369-360(-0.275637355817)`

`(AC)^(2)=369+99.22944809412`

`(AC)^(2)=468.22944809412`

Upon taking square root of both sides of our equation we will be get,

`AC=√(468.22944809412)`

`AC=21.6386101238993629\approx 21.64`

Therefore, the length of b is 21.64 and option B is the correct choice.