What Would be the Answer to tan(60)=7(over)x?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. One of the fundamental trigonometric functions is the tangent, often denoted as tan(θ), which relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle. In this blog post, we will explore how to solve for x in the equation tan(60°) = 7/x.

What Would be the Answer to tan(60)=7(over)x?

The answer to the equation tan(60°) = 7/x is x = 7/√3 or x ≈ 4.041.

Understanding the Equation

Let’s start by breaking down the equation: tan(60°) = 7/x.

1. Tan(60°): In trigonometry, we often work with common angles like 30°, 45°, and 60°. The tangent of 60° is a well-known value. It’s equal to √3, which is approximately 1.732.
2. 7/x: This part of the equation involves an unknown variable, x, and a constant, 7.

The equation tan(60°) = 7/x can be interpreted as follows: “The tangent of 60 degrees is equal to 7 divided by x.”

Solving for x

To solve for x, we need to isolate it on one side of the equation. Here’s how we can do that step by step:

1. Start with the equation: tan(60°) = 7/x.
2. Substitute the value of tan(60°), which is √3: √3 = 7/x.
3. Now, we want to isolate x. To do that, we can cross-multiply:√3 * x = 7.
4. To solve for x, divide both sides of the equation by √3:x = 7/√3.

Rationalizing the Denominator

The expression x = 7/√3 is a valid solution, but it’s often helpful to rationalize the denominator. Rationalizing means modifying the expression to get rid of the square root in the denominator. To do this, multiply both the numerator and denominator by the conjugate of √3, which is √3 itself:

x = (7/√3) * (√3/√3).

This simplifies to:

x = (7√3) / 3.

So, the value of x in the equation tan(60°) = 7/x is x = (7√3) / 3.

Conclusion

In this blog post, we’ve explored how to solve for x in the equation tan(60°) = 7/x. Through a step-by-step process, we found that x is equal to (7√3) / 3. Trigonometric equations like this one are essential in various fields, including physics, engineering, and computer science. Understanding how to manipulate and solve such equations is a valuable skill for anyone working with angles and triangles in real-world applications.