Understanding the Right Triangle
In a right triangle, we have three sides: the opposite side, the adjacent side, and the hypotenuse. To find the length of side AB, we first need to understand the relationship between the tangent function and the sides of the triangle.
The Tangent Function
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In our case, we are given that tan(A) = 0.45.
This can be expressed mathematically as:
tan(A) = Opposite / Adjacent
Setting Up the Equation
Let’s assign values to the sides for simplicity. We’ll let the adjacent side (let’s call it BC) have a length of 1 unit. Then we can use the tangent definition:
tan(A) = Opposite / 1 = 0.45
This means the length of the opposite side (which we’ll call AB) can be calculated as:
AB = tan(A) * Adjacent = 0.45 * 1 = 0.45 units
Calculating the Length
Thus, the approximate length of side AB is 0.45 units. If BC were longer, let’s say 2 units, then:
AB = tan(A) * 2 = 0.45 * 2 = 0.9 units
This calculation demonstrates that the length of AB will scale proportionally with the length of the adjacent side.
Conclusion
To summarize, based on the tangent value of 0.45, the length of side AB varies directly with the length of the adjacent side. For an adjacent side length of 1 unit, AB is approximately 0.45 units.