The base of an isosceles triangle is 10 cm, and the lateral side is 13 cm. Find the sine, cosine, tangent and cotangent

The base of an isosceles triangle is 10 cm, and the lateral side is 13 cm. Find the sine, cosine, tangent and cotangent of the angle between the side of the triangle and the height drawn to its base.

To solve this problem, remember that the sine is equal to the ratio of the opposite leg to the hypotenuse, the cosine is equal to the ratio of the adjacent leg to the hypotenuse, the tangent is the ratio of the opposite leg to the adjacent leg, the cotangent is equal to the ratio of the adjacent leg to the opposite leg. In this triangle, the height divides the base in half. Thus, we get a right-angled triangle with a leg 10/2 = 5 cm, a hypotenuse of 13 cm. Let’s calculate the length of the second leg using the Pythagorean theorem. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs. Let the unknown leg-x cm.
13 ^ 2 = x ^ 2 + 5 ^ 2;
169 = x ^ 2 = 25;
x ^ 2 = 169-25;
x ^ 2 = 144;
x = 12 cm.
sin a = 5/13;
cos a = 12/13;
tg a = 5/10 = 1/2;
ctg a = 12/5 = 2.4.
Answer: 5/13; 12/13; 1/2; 2.4.