In an isosceles triangle ABC In an isosceles triangle ABC In an isosceles triangle ABC, the base length

| August 3, 2021 | education

In an isosceles triangle ABC In an isosceles triangle ABC In an isosceles triangle ABC, the base length of AB is √2, the base angle is 30 degrees. find the perimeter of the triangle.

Let’s build the height BH of the isosceles triangle ABC.

Since the triangle ABC is isosceles, the height of the BH will also be its median, and therefore AH = CH = AC / 2 = √2 / 2 cm.

In a right-angled triangle ABH, by angle A and leg AH, we determine the length of the hypotenuse AB.

Cos30 = AH / AB.

AB = AH / Cos30 = (√2 / 2) / (√3 / 2) = √2 / √3 = √6 / 3 cm.

BC = AB = √6 / 3, since triangle ABC is isosceles, then the perimeter of triangle ABC will be equal to:

P = 2 * AB + AC = 2 * √6 / 3 + √2 = √2 * (1 + 2 * √3 / 3) cm.

Answer: The perimeter of triangle ABC is equal to √2 * (1 + 2 * √3 / 3) cm.



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