In triangle ABC AC = BC, AB = 32 cm, cos⁡A = 0.8. Find AC.

In triangle ABC it is known:

AC = BC;
AB = 32 cm;
cos ⁡ A = 0.8.
Find AC. We express the answer in cm.

Decision:

1) The height in CM of an isosceles triangle divides the AB side in half.

We get:

AM = AB / 2 = 32 cm / 2 = 32/2 cm = 16 cm;

2) AFM triangle.

Angle M = straight.

cos A = AM / AC;

From here we will express what AC is equal to.

AC = AM / cos a;

Substitute the known values and calculate the AC side of the ABC triangle.

In the AMC triangle, the AC side is the hypotenuse.

We get:

AC = AM / cos a = 16 cm / 0.8 = 16 / 0.8 cm = 16 / (8/10) cm = 16 / (4/5) cm = 16 * 5/4 cm = 16/4 * 5 cm = 4 * 5 cm = 20 cm;

Answer: AC = 20 cm.