# Find the base of an isosceles triangle if the base angle is 30 degrees and the height to the base is 10 Find the base.

1. The vertices of the triangle A, B, C. BE = 10 units of measurement – height. ∠А = 30 °.

2. Triangle ABE is rectangular, since the height BE forms an angle AEB equal to 90 ° with the AC side. BE in this triangle is the leg opposite to A equal to 30 °. Therefore, the hypotenuse AB = 2BE = 2 x 10 = 20 units of measurement.

3. Calculate the length of the segment AE, using the formula of the Pythagorean theorem to calculate:

AE = √AB² – BE² = √20² – 10² = √400 – 100 = √300 = 10 √3 units.

4. The height BE in the isosceles triangle ABC also performs the functions of the median and divides the base of the AC into two segments of equal length.

Therefore, AC = AE + CE = 10√3 + 10√3 = 20√3 units of measurement.

Answer: the length of the AC (base of a given triangle) is 20√3 units of measurement.