Question

Calculate the length b to two decimal places.

Answer 1

Answer:

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,

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

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

$(AC)^{2}=369-360(-0.275637355817)$      

$(AC)^{2}=369+99.22944809412$    

$(AC)^{2}=468.22944809412$

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

$AC=\sqrt{468.22944809412}$

$AC=21.6386101238993629\approx 21.64$  

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