The height CD is drawn in a right-angled triangle with a right angle c. It is known that BD = 16cm
The height CD is drawn in a right-angled triangle with a right angle c. It is known that BD = 16cm, CD = 12cm. Find AB, CB, AC, AD.
In a right-angled triangle BCD, according to the Pythagorean theorem, we determine the length of the hypotenuse BC.
ВС ^ 2 = ВD ^ 2 + СD ^ 2 = 256 + 144 = 400.
BC = 20 cm.
Let us prove that triangles ВСD and АСD are similar.
Let the angle CAD = X0, then the angle ACD = (90 – X) 0.
In a triangle ВСD, the angle ВСD = (90 – АСD) = (90 – (90 – X) = X0.
Then triangles ВСD and АСD are similar in acute angle.
Then, in similar triangles:
CD / BD = AD / CD.
CD ^ 2 = AD * BD.
AD = CD ^ 2 / BD = 144/16 = 9 cm.
Then AB = AD + BD = 9 + 16 = 25 cm.
In a right-angled triangle CAD, according to the Pythagorean theorem, AC ^ 2 = CD ^ 2 + AD ^ 2 = 144 + 81 = 225.
AC = 15 cm.
Answer: AB = 25 cm, CB = 20 cm, AC = 15 cm, AD = 9 cm.