In triangle ABC it is known that AB = 17cm, BC = 9cm, angle C is obtuse, height AD = 8cm. Find the side of the speaker.

The ADB triangle is rectangular, since AD is the height of the ABC triangle.

Let the length of the segment CD = X cm, then the length of the segment BD = (9 + X) cm.

By the Pythagorean theorem, from the triangle ABD, AB ^ 2 = AD ^ 2 + BD ^ 2.

172 = 82 + (9 + X) ^ 2.

289 = 64 + 81 + 18 * X + X ^ 2.

X ^ 2 + 18 * X – 144 = 0.

Let’s solve the quadratic equation.

X1 = -24. (Does not fit, since it is negative).

X2 = CD = 6 cm.

In a right-angled triangle ACD, according to the Pythagorean theorem, we determine the length of the leg AC.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 64 + 36 = 100.

AC = 10 cm.

Answer: The length of the AC side is 10 cm.