In triangle ABC, angle C is equal to 45 centimeters and height A D divides the side of CB into segments

In triangle ABC, angle C is equal to 45 centimeters and height A D divides the side of CB into segments CD = 8 centimeters BC = 6 centimeters. Find the area of the triangle and the height to the side AC = 10 cm.

Since AD is elevation, triangle CAD is rectangular, then:

AD = CD * tg (C);

AD = 8 * tg (45) = 8 cm.

Then the area S is equal to:

S = 1/2 * (CD + DB) * AD = 1/2 * (6 + 8) * 8 = 56 cm ^ 2.

The area of a triangle can be expressed as follows:

S = 1/2 * AC * h.

Then:

h = 2 * S / AC = 2 * 56/10 = 11.2 cm.