Question

Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the measure of Y to the nearest whole degree?

58° 64° 68° 73°

Answer 1

use law of cosine: 16²=17²+12²-2*17*12cosY
408cosY=17²+12²-16²=177
cosY=177/408
use your calculator to find Y: Y≈64

Answer 2

Answer: The correct option is second, i.e., 64 degree.

Explanation:

From the given figure it is noticed that the length of three sides are 17,12 and 16.

The law of cosine is defined as,

$a^2=b^2+c^2-2bc\cos A$

Where a,b,c are length of sides and A is the interior angle on vertex A.

We have to find the measure of Y.

$(xz)^2=(xy)^2+(yz)^2-2(xy)(yz)\cos Y$

$\cos Y=\frac{(17)^2+(12)^2-(16)^2}{2(17)(12)}$

$\cos Y=\frac{289+144-256}{408}$

$\cos Y=\frac{177}{408}$

$\cos Y=0.43382$

$Y=\cos^{-1}(0.43382)$

$Y=64.2897\approx 64$

Therefore the second option 64 degree is correct.