The angles of a triangle are in the ratio 1 : 2 : 3, then find the ratio of the corresponding sides.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 1 : √3 : 2
Let the angles of the triangle be x, 2x, and 3x.
Since the sum of the angles in a triangle is 180°, we have:
⇒ x + 2x + 3x = 180° 6x = 180° x = 30°
Therefore, the angles of the triangle are 30°, 60°, and 90°.
Now, we can use the sine rule to find the ratio of the corresponding sides:
⇒ a/sin A = b/sin B = c/sin C
where a, b, and c are the sides of the triangle opposite to angles A, B, and C, respectively.
Substituting the values, we get:
⇒ a/sin 30° = b/sin 60° = c/sin 90°
⇒ a/(1/2) = b/(√3/2) = c/1
a = b√3 = 2c
Therefore, the ratio of the corresponding sides is 1 : √3 : 2.