Question

Find the value of a. Round your answer to the nearest tenth. B 10 77.5 A C 7.9

Answer 1

`\displaystyle 11,3`

Explanation:

Use the Law of Cosines to find the length of the third edge:

Solving for Angles

`\displaystyle (a^2 + b^2 - c^2)/(2ab) = cos\angle{C} \\ (a^2 - b^2 + c^2)/(2ac) = cos\angle{B} \\ (-a^2 + b^2 + c^2)/(2bc) = cos\angle{A}`

Use
`\displaystyle cos^(-1)`towards the end or you will throw your result off!

Solving for Edges

`\displaystyle b^2 + a^2 - 2ba\:cos\angle{C} = c^2 \\ c^2 + a^2 - 2ca\:cos\angle{B} = b^2 \\ c^2 + b^2 - 2cb\:cos\angle{A} = a^2`

Take the square root of the final result or it will be thrown off!

Let us get to wourk:

`\displaystyle 10^2 + 7,9^2 - 2[10][7,9]\:cos\:77,5 = a^2 \hookrightarrow 100 + 62,41 - 158\:cos\:77,5 = a^2 \hookrightarrow √(128,212541) = √(a^2); 11,323097677... \\ \\ \boxed{11,3 \approx a}`

I am joyous to assist you at any time.