Question

In ABC, BC=4 cm, angle b=angle c, and angle a=20 degrees, what is ac to two decimal places

Answer 1

Answer:

Therefore,

$AC=11.52\ cm$

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°.

$\angle a+\angle b+\angle c=180\\\therefore 2m\angle b =180-20=160\\m\angle b=\dfrac{160}{2}=80\°$

We know in a Triangle Sine Rule Says that,  

In Δ ABC,

$\dfrac{a}{\sin A}= \dfrac{b}{\sin b}= \dfrac{c}{\sin C}$

substituting the given values we get

$\dfrac{BC}{\sin a}= \dfrac{AC}{\sin b}$

$\dfrac{4}{\sin 20}= \dfrac{AC}{\sin 80}\\\\AC=11.517=11.52\ cm$

Therefore,

$AC=11.52\ cm$

Answer 2

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,

$\frac{BC}{sin 20} = \frac{AB}{sin 80} = \frac{AC}{sin 80}$

$\frac{4}{0.342} = \frac{AC}{0.984}$                       ( sin 20 = 0.342  & sin 80 = 0.984 )

AC = 11.518 cm