# Right Triangle Trigonometry Problem: Finding Angle x

## Which triangle has an angle equal to arctan(3.1/5.2)?

To determine which triangle has an angle equal to arctan(3.1/5.2), we need to understand the relationship between trigonometric functions and the sides of a right triangle.

The tangent function (tan) is defined as the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle. In this case, arctan(3.1/5.2) represents the angle whose tangent is 3.1/5.2.

Considering the given options:

a. In this triangle, the side adjacent to the right angle is 3.1 and the hypotenuse is 5.2. The angle between these two sides is not x. Therefore, option a can be ruled out.

b. In this triangle, the side adjacent to the right angle is 3.1, and the angle opposite to that side is x. This matches the angle for which we need to find the tangent. Hence, option b is the correct choice.

c. In this triangle, the side opposite the angle x is 3.1, and the hypotenuse is 5.2. This does not match the given tangent value. Thus, option c can be eliminated.

d. In this triangle, the side opposite the angle x is 3.1, and the side adjacent to the right angle is 5.2. This does not correspond to the given tangent value. Therefore, option d is incorrect.

## Answer:

The correct triangle in which the value of x is equal to arctan(3.1/5.2) is **option b**.

Trigonometry involves the study of relationships between the sides and angles of triangles. In a right triangle, the tangent function can help us determine the angles based on the lengths of the sides.

In this particular problem, we are looking for the angle x in a right triangle where the side adjacent to the right angle is 3.1 and the hypotenuse is 5.2. By calculating arctan(3.1/5.2), we can find the angle that corresponds to this tangent ratio.

By analyzing the given options, we can see that only option b aligns with the required angle calculation. Therefore, the correct choice is indeed option b.