In an isosceles triangle, the side is 5cm, and its base is 8cm. Find the height to the base of the triangle.
July 29, 2021 | education|
Since the triangle is isosceles, then its sides are equal – by definition. Therefore, AB = BC = 5 centimeters. The base is 8 centimeters long.
Let’s draw from the top BH to the base of the AC.
The height BH is also the bisector and median of this triangle, by the property of a straight line drawn from a vertex in an isosceles triangle.
AH = HC = 8/2 = 4 centimeters – by the property of the median.
Angle BHA = angle BHC = 90 ° – according to the property of height.
By the Pythagorean theorem, we find the length of the height:
AB ^ 2 = AH ^ 2 + BH ^ 2;
BH ^ 2 = AB ^ 2 – AH ^ 2;
BH ^ 2 = 5 ^ 2 – 4 ^ 2;
BH ^ 2 = 25 – 16;
BH ^ 2 = 9;
BH = 3.
Answer: BH = 3 centimeters.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.