In a right-angled triangle ABC, angle C = 90 degrees, AC = 24 cm, angle B = 60 degrees.
| September 7, 2021 | education
In a right-angled triangle ABC, angle C = 90 degrees, AC = 24 cm, angle B = 60 degrees. BC extended beyond vertex B to segment BD so that BD = AB find AD
Let us determine the length of the hypotenuse AB.
SinABC = AC / AB.
AB = AC / SinABC = 24 / (√3 / 2) = 48 / √3 = 16 * √3 cm.
By condition, BD = AB = 16 * √3 cm, then triangle ABD is isosceles.
The angle ABD is adjacent to the angle ABC, the sum of which is 180, then the angle ABD = 180 – 60 = 120.
By the cosine theorem, we define the length of the side AD.
AD ^ 2 = AB ^ 2 + BD ^ 2 – 2 * AB * BD * Cos120 = 768 + 768 – 2 * 768 * (-1/2) = 2304.
AD = 48 cm.
Answer: The length of the segment AD is 48 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.
