In triangle ABC, angle C = 90, AC = 5, AB = √41. Find tgа

1. Calculate the length of the BC leg. For the calculation, we use the Pythagorean theorem:

BC = √AB² – AC² = √ (√41) ² – 5² = √41 – 25 = √16 = 4 units.

2. We calculate the tangent ∠А – the ratio of the leg BC (located opposite the specified angle) to the leg

AC, which is a side of the specified angle (adjacent to it:

Tangent ∠A = BC / AC = 4/5.

Answer: tangent ∠A = 4/5.