In triangle ABC, angle C is 90 degrees BC = 12 AC = 16 find cosA.

By the condition of the problem, we know that the angle С is equal to 90 degrees.

In this case, we have a right-angled triangle ABC, in which:

AB is the hypotenuse of the triangle;
BC – the first leg of the triangle is 12 cm;
AC – the second leg of the triangle is 16 cm.
Since the legs of a triangle are multiples, we can simplify their meanings.

To do this, divide each of the legs by the largest multiple, which is 4.

In this case, we get:

BC = 12/4 = 3 cm.

AC = 16/4 = 4 cm.

By the Pythagorean theorem, it is known that if the first leg is 3 and the second is 4, then the hypotenuse of the triangle will be 5.

In order to find cosA, you need to divide the value of the opposite leg by the hypotenuse.

We get:

cosA = AC / AB = 16/20 = 4/5 = 0.8.

Answer:

cosA = 0.8.

Solution by the Pythagorean theorem
First, we find the hypotenuse of the right-angled triangle.

To do this, we sum up the squares of the legs.

We get:

C ^ 2 = A ^ 2 + B ^ 2.

C ^ 2 = 16 * 16 + 12 * 12 = 256 + 144 = 400 /

C = 20 cm.

Find the value of cosA.

To do this, divide the value of leg A by hypotenuse C.

We get:

cosA = 16/20 = 4/5 = 0.8.