In a right-angled triangle ABC, the hypotenuse AB = 10, AC = 5. Find the second leg and sharp corners 2.

In a right-angled triangle ABC, the hypotenuse AB = 10, AC = 5. Find the second leg and sharp corners 2. Find an acute angle between the diagonals of a rectangle with sides 12 and 8 cm

We find the second leg of a right-angled triangle according to the Pythagorean theorem as the square root of the difference between the square of the hypotenuse and the square of the known leg, the angles from the ratio of the opposite leg to the hypotenuse.

CB = √ (AB ^ 2 – AC ^ 2) = √ (10 ^ 2 – 5 ^ 2) = √ (100 – 25) = √75 = √ (25 * 3) = 5√3.

sin∠A = CB / AB = 5√3 / 10 = √3 / 2;

∠A = 60 °.

sin∠B = AC / AB = 5/10 = 1/2.

∠B = 90 ° – 60 ° = 30 °.

Answer: CB = 5√3; ∠A = 60 °; ∠B = 30 °.