Respuesta :
Answer:
Therefore,
[tex]AC=11.52\ cm[/tex]
Step-by-step explanation:
Given:
In ΔABC, BC=4 cm,
angle b=angle c, and
angle a=20°
To Find:;
AC = ?
Solution:
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle a+\angle b+\angle c=180\\\therefore 2m\angle b =180-20=160\\m\angle b=\dfrac{160}{2}=80\°[/tex]
We know in a Triangle Sine Rule Says that,
In Δ ABC,
[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin b}= \dfrac{c}{\sin C}[/tex]
substituting the given values we get
[tex]\dfrac{BC}{\sin a}= \dfrac{AC}{\sin b}[/tex]
[tex]\dfrac{4}{\sin 20}= \dfrac{AC}{\sin 80}\\\\AC=11.517=11.52\ cm[/tex]
Therefore,
[tex]AC=11.52\ cm[/tex]
Answer:
AC = 11.518 cm
Step-by-step explanation:
Given ,
BC = 4 cm
∠ b = ∠ c = x ( say )
∠ a = 20°
AC = ?
From the given data it is known that Δ ABC is isosceles triangle and we know that sum of angles of a triangle is 180° .
⇒ ∠ a + ∠ b + ∠ c = 180°
⇒ 20° + x + x = 180°
⇒ 2x = 160°
⇒ x = 80 °
∴ ∠ b = ∠ c = 80°
Now by applying sine rule,
[tex]\frac{BC}{sin 20} = \frac{AB}{sin 80} = \frac{AC}{sin 80}[/tex]
[tex]\frac{4}{0.342} = \frac{AC}{0.984}[/tex] ( sin 20 = 0.342 & sin 80 = 0.984 )
AC = 11.518 cm
