Respuesta :

Medunno13

Answer:

[tex]\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]

Step-by-step explanation:

In triangle ABD,

[tex]\sin 72^{\circ}=\frac{BD}{8} \implies BD=8 \sin72^{\circ} [/tex]

In triangle BCD,

∠CBD=34° (isosceles triangle)

∠DCB=116° (sum of angles in a triangle)

[tex]\frac{BC}{\sin 34^{\circ}}=\frac{8\sin 72^{\circ}}{\sin 116^{\circ}} \\ \\ BC=\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]

Answer:

4.59 cm to nearest hundredth.

Step-by-step explanation:

Consider triangle ABD.

sin 72 = DB / 8

DB = 8 sin 72

      = 7.608 cm.

Imagine a line from point C perpendicular to DB at point E.

As triangle CDB is isosceles ( DC = BC), this line will cut DB in 2

so, DE = 1/2 * 7.608 = 3.804.

Now consider triangle DCE which is a right-angled triangle at E.

cos 34 = 3.804 / DC

DC = 3.804 / cos 34

      = 4.588 cm

BC = DC = 4.588.

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