Respuesta :

mathstudent55

Answer:

b = 8sqrt(3)

Step-by-step explanation:

The triangle has a 30-deg angle and a right angle, so the third angle measures 60 degrees making this a 30-60-90 degree right triangle.

You don't mention which method to use to solve the problem.

You can use trigonometry ratios or the ratios of the lenghts of the sides of a 30-60-90 triangle

I'll use the second method.

In a 30-60-90 triangle, the lengths of the sides are in the ratio:

1 : sqrt(3) : 2

The long leg measures 12 and corresponds to sqrt(3) in the ratio, so we can find the length of the short leg by dividing 12 by sqrt(3).

12/sqrt(3) = [4 * sqrt(3) * sqrt(3)]/sqrt(3) = 4sqrt(3)

The hypotenuse is twice the length of the short leg.

b = 2 * 4sqrt(3) = 8sqrt(3)

The value of b is 8√3 because cos is the ratio of side adjacent to the angle to side opposite to the angle.

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

We have a right angle triangle shown in the picture.

From the cos ratio:

cos30 = 12/b

b = 12/cos30

b = 12/(√3/2)

After factorization:

b = (24√3)/3

b = 8√3

Thus, the value of b is 8√3 because cos is the ratio of side adjacent to the angle to side opposite to the angle.

Learn more about the right angle triangle here:

brainly.com/question/3770177

#SPJ2