In triangle ABC, angle B = 45 degrees, height AN divides the side of BC into segments BN

In triangle ABC, angle B = 45 degrees, height AN divides the side of BC into segments BN = 8cm and CN = 6cm. Find the area of a triangle.

Given:
triangle ABC,
angle B = 45 degrees,
АN – height,
BN = 8 centimeters,
СN = 6 centimeters.
Find the area of the triangle ABC, that is, S ABC -?
Solution:
1. Consider a right-angled triangle ABN. Since the sum of the degree measures of the angles of the triangle is 180 degrees, the angle BAN = 180 – 90 – 45 = 45 (degrees). Then the angle ABN is isosceles. So AN = BN = 8 centimeters.
2. Consider the triangle ABC. BC side = 8 + 6 = 14 (centimeters).
S ABC = 1/2 * AN * BC;
S ABC = 1/2 * 8 * 14;
S ABC = 4 * 14;
S ABC = 56 cm ^ 2.
Answer: 56 cm ^ 2.