# In triangle ABC, angle C = 90 degrees, AB = 55, BC = 33. Find cosine A.

July 28, 2021 | education

| The cosine of an angle in a right-angled triangle is the ratio of the adjacent leg to the hypotenuse. In our case:

Cos A = AC / AB.

The adjacent leg of the AC is unknown, we find it using the Pythagorean theorem:

AC = √ (AB² – BC²) = √ (55² – 33²) = √ (3025 – 1089) = √1936 = 44.

Let’s find what the cosine of the angle A is equal to:

Cos A = AC / AB = 44/55 = 4/5 = 0.8.

Answer: the cosine of angle A is 0.8.

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