Respuesta :
Answer:
84 degrees
Step-by-step explanation:
Applying the Cosine Rule (Choice 2 is the correct one) :-
12^2 = 11^2 + 6^2 - 2*11*6 cos Y
144 = 121 + 36 - 132 cos Y
cos Y = (121 + 36 - 144) / 132
cos Y = 0.09848
Y = 84.3 degrees
Answer:
The measure of angle Y is 84°.
Step-by-step explanation:
The side of a triangle are 6, 11, and 12.
Keyla uses the law of cosines to find the measure of the largest angle.
Law of cosine:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]
where, a,b, c are sides and A is angle.
Let a=12, b=11, c=6 and angle A=\angle Y
Using law of cosine, we get
[tex](12)^2=(11)^2+(6)^2-2(11)(6)\cos Y[/tex]
[tex]144=121+36-132\cos Y[/tex]
[tex]144=157-132\cos Y[/tex]
Subtract 157 from both sides.
[tex]144-157=-132\cos Y[/tex]
[tex]-13=-132\cos Y[/tex]
Divide both sides -132.
[tex]\frac{-13}{-132}=\cos Y[/tex]
[tex]\frac{13}{132}=\cos Y[/tex]
Taking cos⁻¹ both sides.
[tex]\cos ^{-1}\frac{13}{132}=Y[/tex]
[tex]Y\approx 84.348[/tex]
[tex]Y\approx 84^{\circ}[/tex]
Therefore the measure of angle Y is 84°.
