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.
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