How do you use the law of cosines or law of sines if you are given a = 4, b = 3 and c = 6?

Question

2565 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-20T21:25:44

You can use the Law of Cosines to calculate the angles of the triangle.

$A~~36.3$ degrees
$B~~117.3$ degrees
$C~~26.4$ degrees

In this case the only thing you need to solve this triangle is to calculate the angles.

To calculate angle $A$ you use:

$a^2=b^2+c^2-2*b*c*cosA$
so you calculate:

$4^2=3^2+6^2-2*3*6*cosA$
$16=9+36-36cosA$
$36cosA=9+36-16$
$36cosA=29$
$cosA=29/36$
$A~~36.3$ degrees

The same way you can calculate C

$c^2=a^2+b^2-2*a*b$
$6^2=3^2+4^2-2*3*4*cosC$
$36=9+16-24cosC$
$36-9-16=-24cosC$
$11=-24cosC$
$cosC=-11/24$
$C~~117.3$ degrees.

Now you can calculate B either using the Law of Cosines again or using the fact, that the sum of angles in triangle equals to 180 degrees.

$A+B+C=180$
$36.3+B+117.3=180$
$B=180-117.3-36.3$
$B~~26.4$