Answer:
68.8
Explanation:
Solution Method 1:
‾
Solution Method 1:
Use altered formula
�
2
=
�
2
+
�
2
−
2
�
�
cos
�
a
2
=b
2
+c
2
−2bccosA
From reference sheet.
Solve for
cos
�
:
Solve for cosA:
cos
�
=
�
2
+
�
2
−
�
2
2
�
�
cosA=
2bc
b
2
+c
2
−a
2
Since we are finding
∠
�
,
Since we are finding ∠F,
plug in
3.1
for side
�
:
plug in 3.1 for side a:
Opposit the angle we want
cos
�
=
2
2
+
3.
2
2
−
3.
1
2
2
(
2
)
(
3.2
)
cosF=
2(2)(3.2)
2
2
+3.2
2
−3.1
2
Plug in
cos
�
=
4.63
12.8
cosF=
12.8
4.63
Evaluate numerator and denominator
cos
�
=
0.3617188
cosF=0.3617188
Divide (no rounding yet)
�
=
cos
−
1
(
0.3617188
)
≈
68.7942
≈
68.
8
∘
F=cos
−1
(0.3617188)≈68.7942≈68.8
∘
Solution Method 2:
‾
Solution Method 2:
Use original formula
�
2
=
�
2
+
�
2
−
2
�
�
cos
�
a
2
=b
2
+c
2
−2bccosA
From reference sheet.
Since we are finding
∠
�
,
Since we are finding ∠F,
plug in
3.1
for side
�
:
plug in 3.1 for side a:
Opposit the angle we want
3.
1
2
=
2
2
+
3.
2
2
−
2
(
2
)
(
3.2
)
cos
�
3.1
2
=2
2
+3.2
2
−2(2)(3.2)cosF
Plug in values. Side "a" is opposite the wanted angle.
9.61
=
4
+
10.24
−
12.8
cos
�
9.61=4+10.24−12.8cosF
Square sides.
9.61
=
9.61=
−
14.24
−
12.8
cos
�
−14.24−12.8cosF
Add.
−
14.24
=
−14.24=
−
14.24
−14.24
−
4.63
=
−4.63=
−
12.8
cos
�
−12.8cosF
−
4.63
−
12.8
=
cos
�
−12.8
−4.63
=cosF
Divide to solve for cos(A).
�
=
cos
−
1
(
−
4.63
−
12.8
)
≈
68.794
≈
68.
8
∘
F=cos
−1
(
−12.8
−4.63
)≈68.794≈68.8
∘
Use inverse cosine to find the angle then round.