In an isosceles triangle ABC AB = BC, the base is 12 cm, and the height projected to it is 8 cm.

In an isosceles triangle ABC AB = BC, the base is 12 cm, and the height projected to it is 8 cm. Find the sines, cosines, tangents of the angles at the base.

Since in the triangle ABC, by condition, AB = BC, the triangle ABC is isosceles, and therefore the angles at the base of the AC are equal, the angle BAC = BCA.

The height of the ВH of the triangle ABC is also its median, then AH = CH = AC / 2 = 12/2 = 6 cm.

In a right-angled triangle ABН, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = BH ^ 2 + AH ^ 2 = 64 + 36 = 100.

AB = 10 cm.

Determine the sine, cosine and tangent of the ВAН angle.

tgVAN = ВН / AН = 8/6 = 4/3 = 1 (1/3).

CosVAN = AН / AB = 6/10 = 0.6.

SinVAN = ВН / AB = 8/10 = 0.8.

Answer: tgBAC = 1 (1/3), CosВAН = 0.6, SinВAН = 0.8.