Question

In ΔABC, AB=6√3 cm, AC=12 cm, BC = 6 cm. Find measure of ∠A.
(A) 30°
(B) 60°
(C) 90°
(D) 45°

Answer 1

30 degree will be the answer

Answer 2

Answer:

(A) 30°

Step-by-step explanation:

Given,

In triangle ABC

$AB\ =\ 6\sqrt{3}$

AC = 12 cm

and BC = 6 cm

From the given data we have,

$AC^2\ =\ 12^2\ =\ 144$

$BC^2\ +\ AB^2\ =\ 6^2\ +\ (6\sqrt{3})^2\ =\ 144$

Hence, we can see that

$AC^2\ =\ AB^2\ +\ BC^2$

So, the given triangle ABC is a right angle triangle. So, we cam write that

$tanA\ =\ \dfrac{perpendicular}{base}$

          $=\ \dfrac{6}{6\sqrt{3}}$

         $=\ \dfrac{1}{\sqrt{3}}$

So, we can write

∠A = 30°

So, the measurement of angle A of triangle ABC is 30°.