In a right-angled triangle ABC AC = BC Find the length of the hypotenuse if the height drawn to it is 18 cm.
September 25, 2021 | education
| AC and BC – legs, are equal by condition, so triangle ABC is isosceles, angles A and C are equal, CD is height.
The sum of the angles in the triangle is 180 °, we find the angle A:
A + B + C = 180 °.
2 × A = 180 ° – 90 °;
A = 90 °: 2 = 45 °
Let us find the length AD through tg of the angle A – the ratio of the opposite leg to the adjacent one.
In a triangle ACD CD = 18 cm (opposite leg), AD – adjacent
Tg A = CD: AD;
AD = CD × tg A ;;
AD = 18 × 1 = 18 cm.
In an isosceles triangle, the height drawn to the base divides it into two equal segments:
AB = 2 × AD = 2 × 18 = 36 cm
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.