In an isosceles triangle, one of the corners is 120 °, and the base is 36 cm. Find the height drawn to the side.

| December 16, 2020 | education

In an isosceles triangle, the angles at the base are equal. This means that any of the angles at the base cannot be 120 °, because 240 ° (120 ° × 2) is already greater than 180 ° (the sum of the angles of the triangle). So the angle of 120 degrees is the angle above the base (between the sides). Then the sum of the remaining two equal angles = 60 ° (180 ° – 120 °). If they are equal, then each of them is 60 °: 2 = 30 °.
Let’s call our triangle ABC with base AC. Then the height drawn to the lateral side from the vertex A will be called AK. We get a right-angled triangle AKC with a right angle K (since AK is the height).
We know that the base (AC) = 36cm. AC will be the hypotenuse of the triangle AKC, and the height of the AK will be its leg. We found that the angle is C = 30 °. The AK leg lies opposite a 30 ° angle. By property, it is equal to half the hypotenuse. We get that the height of AK = 36: 2 = 18cm.
Answer: 18cm.



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.