My question is in image I have attached. I Want explanation of this question. Answer is tanø but how?

It seems like you're looking for an explanation of why the answer to your question is tan(θ). While I can't see the image you've mentioned, I can help clarify how tan(θ) often arises in various mathematical contexts, particularly in trigonometry. Let's break it down step by step.

Understanding Tangent in Trigonometry

The tangent function, denoted as tan(θ), is one of the primary trigonometric functions. It relates the angle θ in a right triangle to the ratios of the lengths of the opposite side and the adjacent side. Specifically, it is defined as:

• tan(θ) = Opposite / Adjacent

Visualizing the Concept

Imagine a right triangle where:

• The angle θ is one of the non-right angles.
• The side opposite to θ is the "opposite" side.
• The side next to θ (but not the hypotenuse) is the "adjacent" side.

In this triangle, if you know the lengths of the opposite and adjacent sides, you can easily calculate tan(θ). For example, if the opposite side is 3 units long and the adjacent side is 4 units long, then:

• tan(θ) = 3 / 4 = 0.75

Applications of Tangent

Tangent is not just limited to triangles; it also appears in various mathematical contexts, such as:

• Unit Circle: In the unit circle, tan(θ) can be represented as the y-coordinate divided by the x-coordinate of a point on the circle.
• Graphing: The graph of the tangent function has a periodic nature, with vertical asymptotes where the function is undefined.
• Real-world Applications: Tangent is used in physics, engineering, and even in fields like computer graphics to calculate angles and slopes.

Why tan(θ) Might Be the Answer

In many problems, especially those involving angles and triangles, you might be asked to find a relationship that simplifies to tan(θ). This could be due to:

• Finding the slope of a line in a coordinate system.
• Determining the angle of elevation or depression in real-world scenarios.
• Solving equations that involve right triangles or circular functions.

For instance, if your problem involves calculating the slope of a ramp or the angle of a roof, you might find that the relationship simplifies to tan(θ) because of the way the opposite and adjacent sides relate to the angle in question.

Final Thoughts

Understanding why tan(θ) is the answer often comes down to recognizing the relationships between angles and sides in triangles, as well as how these concepts apply in broader mathematical contexts. If you have specific details from the question or any additional context, feel free to share, and I can provide a more tailored explanation!