In triangle ABC, angle C is 90 degrees, AB = 14, cosA = 0.5. find AC

Given a triangle ABC, the angle C is 90 degrees, AB = 14 cm, cos∟A = 0.5.

Find the AC side.

Since ∟C = 90, then AB – hypotenuse, AC and BC – legs.

For a given value of the cosine of the angle, we find the angle itself from the table of values of trigonometric functions of some angles:

if cos∟A = 0.5 then A = 60 degrees.

Then the angle ∟В = 180 – 90 – 60 = 30 degrees.

Then by the property for a right-angled triangle with an angle of 30 degrees:

the opposite leg CA is equal to half of the hypotenuse AB.

Therefore, CA = 1/2 * AB = 1/2 * 14 = 7 (cm).

Answer: CA = 7 cm.