In an acute-angled triangle ABC, angle A is 45 degrees, BC = 13 cm. On the AC side, point D

| March 7, 2021 | education

In an acute-angled triangle ABC, angle A is 45 degrees, BC = 13 cm. On the AC side, point D is taken so that DС= 5 cm, ВD = 12 cm. Prove that triangle ВDС is rectangular and find the area of triangle ABC.

Since all the lengths of the sides of the triangle BCD are given in the condition, we determine the type of the triangle using the Pythagorean theorem, taking the larger side for the hypotenuse.

BC ^ 2 = 13 ^ 2 = 169.

BD ^ 2 + CD ^ 2 = 12 ^ 2 + 5 ^ 2 = 144 + 25 = 169.

ВС ^ 2 = ВD ^ 2 + СD ^ 2, therefore the triangle ВСD is rectangular, as required.

In a right-angled triangle ABD, the angle BAD, by condition, is 45, then the legs of the triangle are equal, AD = BD = 12 cm.

Side length АС = АD + СD = 12 + 5 = 17 cm.

Then Savs = AC * BD / 2 = 17 * 12/2 = 102 cm2.

Answer: The area of the triangle is 102 cm2.



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