In the triangle ABC C = 90, AB = 25, tg A = 4/3. Find the side of the speaker.

1. The tangent of the angle of a right-angled triangle is the ratio of the leg opposite

this angle (opposite), to the leg, which is its side (adjacent). Then

is the tangent ∠A = BC / AC = 4/3.

Therefore, BC: AC = 4: 3.

3BC = 4AC.

BC = 4AC / 3.

2. Calculate the length of the AC leg using the Pythagorean theorem:

AB² = BC² + AC².

3. We substitute in this expression 4АС / 3 instead of ВС:

(4АС / 3) ² + АС² = AB².

16 AC² / 9 + AC² = 625.

25АС² / 9 = 625.

AC² = 9 x 25.

AC = 15 cm.

Answer: the length of the AC leg is 15 centimeters.