In the ABC triangle, the angle C is 135 degrees, AC = 6 cm, the BO height is 2 dm. Find the ABD triangle.

It is known from the condition that in triangle ABC the angle is C = 135 °, AC = 6 cm, and the height of the ВO is 2 dm. We need to find the area of the triangle ABD.

Let’s start by finding the degree measure of angle B.

Angle С = 135 ° (according to the condition). Angle adjacent to angle C in triangle BCD = 45 ° (180 ° – 135 ° = 45 °).

Angle D – straight (90 °). We conclude that the second angle in this triangle is also 45 °, that is, the triangle is isosceles.

Therefore, BD = CD = 2.

It turns out AD = 6 + 2 = 8.

BD = 2AD, by the Pythagorean theorem = 2√17.

Area of triangle ABD:

S = 8 * 2 * 1/2 = 8 sq. units.