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

64

Explanation:

got it right on edge

Answer 2

Therefore A =
`cos^(-1)`(0.4338) = 64.29°

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
`*` 12
`*` 17
`*` cos(A))

⇒ 256 = 144 + 289 - 408cos(A)

⇒ 256 - 144 - 289 = -408cos(A)

⇒ -177 = -408cos(A)

⇒ cos A =
`(-177)/(-408)` = 0.4338

Therefore A =
`cos^(-1)`(0.4338) = 64.29°