In triangle ABC, angle C is 90 degrees, AB = 5, AC = √21. Find cos B.

Find cos B in triangle ABC if the values are known:

Angle C = 90 °;
AB = 5;
AC = √21.
Decision:

1) The hypotenuse AB and leg AC are known in the triangle. Find the second BC leg.

We find the leg BC by the Pythagorean theorem.

BC = √ (AB ^ 2 – AC ^ 2) = √ (5 ^ 2 – (√21) ^ 2) = √ (25 – 21) = √4 = √2 ^ 2 = 2;

2) Find cos B.

cos B = BC / AB (ratio of the adjacent leg to the hypotenuse);

cos B = 2/5 = 0.4.

As a result, we got that cos B = 0.4.

Answer: cos B = 0.4.