In triangle ABC, it is known that angle C = 90 degrees, angle A = 30 degrees, CD-height, BD = 7cm
| June 17, 2021 | education
In triangle ABC, it is known that angle C = 90 degrees, angle A = 30 degrees, CD-height, BD = 7cm. Find the hypotenuse AB.
In a right-angled triangle ABC, we determine the value of the angle ABC.
Angle ABC = (180 – 90 – 30) = 60.
In a right-angled triangle BCD tg60 = CD / BD.
СD = ВD * tg60 = 7 * √3 cm.
The height CD is drawn to the hypotenuse from the top of the right angle, then the square of the height is equal to the product of the segments by which the height divides the hypotenuse.
CD ^ 2 = BD * AD.
АD = СD ^ 2 / ВD = (7 * √3) 2/7 = 21 cm.
The length of the side AB is equal to: AB = AD + BD = 21 + 7 = 28 cm.
Answer: The length of the AB side is 28 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.
