Answer:
4.3
Explanation:
In ΔDEF, d = 6.4 inches, e = 7.8 inches and ∠F=33°. Find the length of f, to the nearest 10th of an inch.
D
E
F
d = 6.4
e = 7.8
33°
S.A.S.
→
Law of Cosines
S.A.S.→Law of Cosines
�
2
=
�
2
+
�
2
−
2
�
�
cos
�
a
2
=b
2
+c
2
−2bccosA
From reference sheet.
�
2
=
6.
4
2
+
7.
8
2
−
2
(
6.4
)
(
7.8
)
cos
33
f
2
=6.4
2
+7.8
2
−2(6.4)(7.8)cos33
Plug in values.
�
2
=
40.96
+
60.84
−
2
(
6.4
)
(
7.8
)
(
0.838671
)
f
2
=40.96+60.84−2(6.4)(7.8)(0.838671)
Square and find cosine.
�
2
=
40.96
+
60.84
−
83.73287
f
2
=40.96+60.84−83.73287
Multiply.
�
2
=
18.06713
f
2
=18.06713
Add.
�
=
18.06713
≈
4.251
≈
4.3
f=
18.06713
≈4.251≈4.3
Square root and round.
Your Solution:
4.3
4.3