2 years ago

Can someone please help me solve this

Mathematics

1 answer:

pentagon [3]2 years ago

5 0

Answer:

Step-by-step explanation:

A segment joining the midpoints of a triangle is

• Parallel to the third side

• Half the length of the third side

The segment DF joins the midpoints of 2 sides of Δ ABC , then

BC = 2 × DF = 2 × 4 = 8

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Given: △ABC; AB=BC, m∠BDA = 60°, BD=4 cm, BD ⊥ BA . Find: DC, AC.

vekshin1

Answer:

DC = 10.93 cm , AC = 9.8 cm

Step-by-step explanation:

From trigonometry;

⇒ Tan 60 = AB/BD

⇒AB = BD Tan 60 ( where BD = 4 cm )

⇒ AB = 6.93 cm

Also, AB=BC , therefore;

⇒ BC = 6.93 cm

⇒ Cos 60 = BD/AD

⇒ AD = BD/ Cos 60 = 4/Cos 60

⇒ AD = 8 cm

From Pythagoras theorem;

⇒ $AC^{2}$ = $AB^{2}$ + $BC^{2}$ = $(6.93)^{2}$ + $(6.93)^{2}$

⇒ AC = $\sqrt{96.05}$ = 9.80 cm

⇒ DC = BD + BC = 4 + 6.93

⇒ DC = 10.93 cm

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