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.

| September 28, 2021 | education

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.



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