Question

Find the length of Line ED Round to the nearest hundredth.

A.
7.32 m
B.
9.48 m
C.
9.56 m
D.
33.80 m

Answer 1

The angles in a triangle add up to 180°.

`m \angle D + m \angle E + m \angle F=180^\circ \\ 54^\circ + m \angle E + 32^\circ = 180^\circ \\ m \angle E=180^\circ - 54^\circ - 32^\circ \\ m \angle E=94^\circ`

According to the law of sines, the ratio of the length of a side of a triangle to the sine of the angle opposite to this side is the same for all sides.
So, the ratio of DF to sin m∠E is the same as the ratio of ED to sin m∠F.

`(18)/(\sin 94^\circ)=(x)/(\sin 32^\circ) \\ \\ (18)/(\sin 94^\circ) * \sin 32^\circ= x \\ \\ (18)/(0.9976) * 0.5299 \approx x \\ \\ x \approx 9.56`

The answer is C.

Answer 2

The correct option is C. 9.56 meter

Explanation:

∠D = 54° , ∠F = 32°

Now, Using angles sum property of a triangle

∠D + ∠F + ∠E = 180°

⇒ 54° + 32° + ∠E = 180°

⇒ ∠E = 180 - 86

⇒ ∠E = 94°

Now, Using sine rule in the triangle DEF

`(FD)/(\sin 94)=(ED)/(\sin 32)\\\\\implies (18)/(\sin 94)=(ED)/(\sin 32)\\\\\implies ED = (18 * \sin 32)/(\sin 94)\approx 9.56\text{ meter}`

Hence, The correct option is C. 9.56 meter