# In a triangle ABC: AC equals BC equals 10 COS A equals 0.4 Find AB.

May 29, 2021 | education

| The following data are known in the ABC triangle:

AC = BC = 10;

cos A = 0.4;

Find AB.

1) Since AC = BC, it means that the triangle is isosceles.

2) CH – the height of the triangle ABC. The height CH divides the side AB of the triangle ABC in half.

3) Consider the ASN triangle.

The triangle is rectangular.

cos A = AH / AC;

AH = AC * cos A;

Substitute the known values into the formula and calculate AH – half of the side AB of triangle ABC.

AH = 10 * 0.4 = 10 * 4 * 0.1 = 10 * 0.1 * 4 = 4;

4) Find the side AB of the triangle ABC.

AB = 2 * AH = 2 * 4 = 8.

Answer: AN = 8.

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