In a triangle ABC, angle C is 90 AB 14 tangent of angle A 20 / 3√3 Find AC.

Since C is equal to 90 degrees, then AB is the hypotenuse of a right-angled triangle, by definition of the tangent we get:

sin (a) / cos (a) = 20/3 * √3.

Let’s square the equation:

cos ^ 2 (a) = sin ^ 2 (a) * 9 * 3/400.

Let’s use the basic trigonometric identity:

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

sin ^ 2 (a) + 27/400 * sin ^ 2 (a) = 1;

sin ^ 2 (a) = 400/427;

sin (a) = 20 / √427.

| AC | = | AB | * sin (a) = 14 * 20 / √427 = 280 / √427.




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