Question

Law of cosines HELP MES

Answer 1

Answer:

70.52 degrees

Step-by-step explanation:

To find the angles, we must first find the lengths of each side of the triangle. Adding up the respective radii, we can see that

XY = 5+4 = 9 CM

XZ = 6+5 = 11 CM

ZY = 4+6 = 10 CM

Now we can apply the cosine rule

$C\:=\:\sqrt{A^2+B^2-2ABcosx}$

We need to rearrange the rule to solve for x, our missing angle

$x\:=\:cos^{-1}\left(\frac{a^2+b^2-c^2}{2ab}\right)$

solving for our unknown angle:

$x\:=\:cos^{-1}\left(\frac{9^2+10^2-11^2}{2\cdot 9\cdot 10}\right)$

$x\:=\:70.52^{\circ }$

Therefore angle YXZ is 70.52 degrees