In an isosceles triangle, the side is 17 cm and the base is 16 cm. Find the height lowered to the base.

An isosceles triangle is a triangle in which the sides are equal:

AB = BC.

The height of an isosceles triangle, lowered to the base, is also the median; it divides the base in half:

AH = HC = AC / 2;

AH = HC = 16/2 = 8 cm.

Consider the triangle ΔАВН. To calculate the length of the VN, we apply the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = BH ^ 2 + AH ^ 2;

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 17 ^ 2 – 8 ^ 2 = 289 – 64 = 225;

BH = √225 = 15 cm.

Answer: the length of the height BH is 15 cm.