The legs of a right triangle are 5 cm and 12 cm find the sine cosine and tangent of the smaller acute angle.

1. A, B, C – the vertices of the triangle. BC = 5 centimeters. AC = 12 centimeters. ∠С = 90 °.

2. We calculate the length of the side AB – the hypotenuse of the given triangle. For the calculation, we use the Pythagorean theorem:

AB = √BC² + AC² = √5² + 12² = √25 + 144 = √169 = 13 centimeters.

3. In a given triangle, the smaller acute angle is ∠A, since it is opposite the smaller side of the BC.

4. We calculate the trigonometric functions ∠А:

Sine ∠A is the ratio of the leg opposite this angle to the hypotenuse.

Sinus ∠A = BC / AB = 5/13.

Cosine ∠A is the ratio of the leg, which is the side of this angle to the hypotenuse.

Cosine ∠A = AC / AB = 12/13.

Tangent ∠A is the ratio of the leg opposite this angle to the leg that is the side of this angle.

Tangent ∠A = BC / AC = 5/12.

Answer: sine A = 5/13, cosine ∠A = 12/13, tangent ∠A = 5/12.