In a right-angled triangle ABC, angle C is straight. Find the hypotenuse AB if AC = root of 21, cosB = 0.4.

In a right-angled triangle ABC it is known:

Angle C – straight;
AC = √21;
cos B = 0.4.
Let’s find the hypotenuse AB.

1) sin ^ 2 b + cos ^ 2 b = 1;

sin ^ 2 b = 1 – cos ^ 2 b;

sin b = √ (1 – cos ^ 2 b);

Substitute the known values and calculate the sine of angle B.

sin b = √ (1 – 0.4 ^ 2) = √ (1 – 0.16) = √0.84 = 2√0.21;

2) cos b = AC / AB;

AB = AC / cos b;

Substitute the known values and calculate the hypotenuse of triangle ABC.

AB = √21 / 2√0.21 = 1/2 * √ (21 / 0.21) = 1/2 * √100 = 1/2 * 10 = 5;

As a result, we got that the hypotenuse of the triangle ABC is equal to AB = 5.