Question

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

Answer 1

AC = 11.518 cm

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,

`(BC)/(sin 20) = (AB)/(sin 80) = (AC)/(sin 80)`

`(4)/(0.342) = (AC)/(0.984)` ( sin 20 = 0.342 & sin 80 = 0.984 )

AC = 11.518 cm

Answer 2

Therefore,

`AC=11.52\ cm`

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=(160)/(2)=80\°`

We know in a Triangle Sine Rule Says that,

In Δ ABC,

`(a)/(\sin A)= (b)/(\sin b)= (c)/(\sin C)`

substituting the given values we get

`(BC)/(\sin a)= (AC)/(\sin b)`

`(4)/(\sin 20)= (AC)/(\sin 80)\\\\AC=11.517=11.52\ cm`

Therefore,

`AC=11.52\ cm`