# The height BD of the triangle ABC divides the base of the AC into segments: AD = 8cm

March 28, 2021 | education

| **The height BD of the triangle ABC divides the base of the AC into segments: AD = 8cm, DC = 12cm, and the angle A at the base of AD is 45 (degrees). find the area.**

Determine the length BD from a right-angled triangle ABD using the definition of the tangent of an angle:

tg BAD = BD / AD;

BD = tan BAD * AD = tan 45 ° * 8 = 1 * 8 = 8 cm.

Find the length of the base of triangle ABC:

AC = AD + DC = 8 + 12 = 20 cm.

Let’s calculate the area of the triangle:

S abc = 1/2 * a * h = 0.5 * AC * BD = 0.5 * 20 * 8 = 80 cm².

Answer: The area of a given triangle is 80 square 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.