The base of an isosceles triangle is 16 cm and the included angle is 30 degrees

The base of an isosceles triangle is 16 cm and the included angle is 30 degrees. 1) Calculate the side. 2) the height drawn to the base. 3) the height drawn to the side

In an isosceles triangle ABC AB and BC are the lateral sides, AC is the base, BH is the height drawn to the base is the bisector and median;

AC = 16 cm; <A = <C = 30 °;

AH = 1/2 AC = 8 cm;

BH = 1/2 AB – leg lying opposite an angle of 30 °; AB = 2 BH;

By the Pythagorean theorem:

AH² = AB² – BH²; AH² = 4 BH² – BH²; BH² = 1/3 AH²; BH² = 1/3 * 64;

BH = √ (64/3); BH = 8 / √3 ≈ 4.62 (cm);

AB = BC = 2 * 4.62 ≈ 9.24 cm;

CK – the height drawn to the side;

In a right-angled triangle ACK KC is a leg lying opposite an angle of 30 °, which means

CK = 1/2 AC = 1/2 * 16 = 8 (cm);