In triangle ABC, angle C = 90 degrees, cos A = 0.8. Find tg a

We have a right-angled triangle. The cosine of the angle is known. To find its tangent, you need to divide the sine of the angle by the cosine.

The sine of an angle is found from the basic trigonometric identity:

sin ^ 2 a + cos ^ 2 a = 1;

sin ^ 2 a = 1 – cos ^ 2 a.

Let’s write an expression for the tangent of an angle and find it:

tan a = sin a / cos a = 1 / cos a * (1 – cos ^ 2 a) ^ (1/2) = (1 / 0.8) * (1 – 0.64) ^ (1/2) = (1 / 0.8) * 0.6 = 6/8 = 3/4.

Answer: 3/4.