In triangle ABC: ∠C = 90 °, BC = 10, AB = 26. Find the tangent of angle B.

In triangle ABC:

∠ С = 90 °;
BC = 10;
AB = 26.
Find the tangent of angle B, that is, tg B.

Decision:

1) Triangle ABC is rectangular. Knowing the hypotenuse AB and one leg BC, we can find the second leg by the Pythagorean theorem.

AB ^ 2 = AC ^ 2 + BC ^ 2;

AC ^ 2 = AB ^ 2 – BC ^ 2;

Substitute the known values and calculate the second leg.

AC ^ 2 = 26 ^ 2 – 10 ^ 2 = (26 – 10) * (26 + 10) = 16 * 36 = 4 ^ 2 * 6 ^ 2 = (4 * 6) ^ 2 = 24 ^ 2;

Hence, AC = 24.

2) Find tg B.

tg B = AC / BC = 24/10 = (2 * 12) / (2 * 5) = 12/5 = 10/5 + 2/5 = 2 + 0.4 = 2.4;

Answer: tg B = 2.4.