The side of an isosceles triangle is 17 cm, and the base is 16 cm. Find the height drawn to the base.

From the condition it is known that the lateral side of an isosceles triangle is 17 cm, and the length of the base is also known – 16 cm.In order to find the height lowered to the base, we will consider a right-angled triangle formed by the lateral side of the triangle, height (has a right angle with the base ) and half the base 16: 2 = 8 cm (since the height in an isosceles triangle is the median and the height).
Let’s apply the Pythagorean theorem:
c ^ 2 = a ^ 2 + b ^ 2;
a ^ 2 = c ^ 2 – b ^ 2;
a = √ (c ^ 2 – b ^ 2) = √ (17 ^ 2 – 8 ^ 2) = √ (289 – 64) = √225 = 15 cm.