In an isosceles triangle ABC, the side length is 10cm and the base length is 12cm.

In an isosceles triangle ABC, the side length is 10cm and the base length is 12cm. Calculate the sine and cosine of the angle at the base of the triangle.

Let’s build the height of the HВ triangle ABC.

Since the triangle ABC, by condition, is isosceles, the height of the ВН is also its median, and therefore, AH = CH = AC / 2 = 12/2 = 6 cm.

Triangle ABH is rectangular, then through the hypotenuse AB and leg AH we define the cosine of the angle BAН adjacent to the leg.

CosBAH = AH / AB = 6/10 = 0.6.

Let us define the sine of the angle BAН through the cosine of this angle.

Sin2BAH + Cos2BAH = 1.

Sin2BAH = 1 – Cos2BAH = 1 – 0.36 = 0.64.

SinBAH = 0.8.

Answer: The cosine of the angle at the base is 0.6, the sine of the angle at the base is 0.8.