In the triangle ABC, the angle is C = 90 degrees, AB = 75, AC = 60. Find the tangent A.

Given:

ABC – right triangle;

Angle C = 90 degrees;

AB = 75;

AC = 60;

Find tg A.

Decision:

In order to find tg A of triangle ABC, we use the formula:

tg A = BC / AC.

Find BC: BC = √ (AB ^ 2 – AC ^ 2) = √ (75 ^ 2 – 60 ^ 2) = √ (5625 – 3600) = √2025 = 45;

Substitute the known values into the formula tg A = BC / AC.

tg A = BC / AC = 45/60 = (5 * 9) / (5 * 12) = 9/12 = (3 * 3) / (3 * 4) = 3/4 = 0.75.

As a result, we got tg A = 0.75.

Answer: tg A = 0.75.