Question

Triangle X Y Z is shown. The length of X Z is 16, the length of Y Z is 12, and the length of Y X is 17. Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the measure of AngleY to the nearest whole degree? 58° 64° 68° 73°

Answer 1

Answer:

64

Step-by-step explanation:

Answer 2

Answer:

Therefore A  =  $cos^{-1}$(0.4338) = 64.29°

Step-by-step explanation:

i) Law of cosines: $a^{2}$ = $b^{2}$ + $c^{2}$ – 2bccos(A)

ii) XZ = a = 16 ,  YZ = b = 12,  XY = 17,     ∠Y  =  ∠A

iii)  $16^{2}$  =  $12^{2}$  + $17^{2}$  - (2$\times$ 12$\times$ 17$\times$ cos(A))

   ⇒    256 = 144 + 289 -  408cos(A)

⇒   256 - 144 -  289  =  -408cos(A)

⇒    -177 = -408cos(A)

⇒    cos A =  $\frac{-177}{-408}$  = 0.4338

Therefore A  =  $cos^{-1}$(0.4338) = 64.29°