Question

The law of cosines is used to find the measure of Q.

242 = 202 + 342 – 2(20)(34)cos(Q)

576 = 400 + 1156 – (1360)cos(Q)

576 = 1556 – (1360)cos(Q)

–980 = –(1360)cos(Q)

To the nearest whole degree, the measure of angle Q _____ is
degrees

Answer 1

the right answer is 44.

Answer 2

44 degrees.

Explanation:

We are asked to find the measure of angle Q using law of cosines.

Law of cosines:

`c^2=a^2+b^2-2ab* cos(C)`

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

`24^2=20^2+34^2-2* 20* 34* cos(Q)`

`576=400+1156-1360* cos(Q)`

`576=1556-1360* cos(Q)`

`576-1556=1556-1556-1360* cos(Q)`

`-980=-1360* cos(Q`

Upon dividing both sides of our equation by -1360 we will get,

`(-980)/(-1360)=(-1360* cos(Q)/(-1360)`

`0.7205882352941176=cos(Q)`

Now we will use arccos to solve for the measure of angle Q.

`cos^(-1)(0.7205882352941176)=Q`

`43.896932391182=Q`

`Q\approx 44`

Therefore, the measure of angle Q is 44 degrees.