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romanna [79]
2 years ago
13

In ΔDEF, e = 2.7 inches, ∠F=49° and ∠D=58°. Find the length of f, to the nearest 10th of an inch.

Mathematics
1 answer:
Anton [14]2 years ago
7 0

Answer:2.1

Step-by-step explanation:

\text{Draw a diagram:}

Draw a diagram:

D

E

F

e = 2.7

f = ?

49°

58°

\text{A.S.A.}\rightarrow \text{Law of Sines}

A.S.A.→Law of Sines

\frac{a}{\sin A}=\frac{b}{\sin B}

sinA

a

​

=

sinB

b

​

\text{Find other angle:}

Find other angle:

\angle E=180-49-58=73^{\circ}

∠E=180−49−58=73

∘

D

E

F

e = 2.7

f = ?

49°

58°

73°

\frac{f}{\sin 49}=\frac{2.7}{\sin 73}

sin49

f

​

=

sin73

2.7

​

f=\frac{2.7\sin 49}{\sin 73} \approx 2.131 \approx 2.1

f=

sin73

2.7sin49

​

≈2.131≈2.1

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