The fascinating field of business coaching has been gaining momentum over the past years in the United States. It has evolved into a structured and highly strategic system that assists entrepreneurs in navigating the complexities of the business world. Notwithstanding, the future holds promise for further advancements and transformations. Thus, it is imperative to discuss the potential trajectories this field might follow, the emerging trends, and the implications for stakeholders.

Firstly, let's delve into who the key players are in this sphere. Business coaches, often with a rich background in entrepreneurship, are the engines that drive this industry. They guide and mentor business owners, helping them realize their business goals efficiently and effectively. Meanwhile, the entrepreneurs, who are seeking to steer their businesses to success, are the beneficiaries of these professional services.

The 'what' of business coaching involves the provision of guidance, support, accountability, and inspiration to entrepreneurs. This is achieved by employing a blend of innovative methodologies and traditional practices. Coaches work closely with clients to identify their strengths, weaknesses, opportunities, and threats, thus aiding them in making informed decisions.

The realm of business coaching is not confined to any particular geographical locale. From bustling cities to remote rural areas, business coaching has made its mark. This is largely facilitated by technological advancements that have rendered geographical barriers obsolete.

The evolution of business coaching has been consistent. It started gaining traction in the late 20th century and has since grown exponentially. The future is likely to witness a steep rise in the demand for business coaches owing to the increasing complexity of the business environment.

The 'how' of business coaching involves a personalized approach tailored to the needs, aspirations, and circumstances of each entrepreneur. Techniques and tools used by coaches vary widely. Traditional methods like face-to-face meetings are being supplemented with digital solutions such as online platforms, video conferencing, and digital tools for tracking progress and maintaining accountability.

The relevance of business coaching lies in its capacity to accelerate the growth and profitability of businesses. It provides entrepreneurs with a fresh perspective, helping them overcome challenges and bottlenecks, and propelling them towards their objectives.

Emerging trends in business coaching indicate a shift towards more technology-based solutions. Coaches are increasingly utilizing Artificial Intelligence (AI) and Machine Learning (ML) to streamline their services and enhance the results. AI can be used to analyze data to identify patterns and forecast trends, providing actionable insights to entrepreneurs. Similarly, ML can be employed to customize the coaching experience for each client based on their unique needs and goals.

Another significant trend is the increasing emphasis on sustainability and social responsibility. Coaches are helping businesses align their strategies with sustainable practices and social good. This not only boosts their reputation but also increases their chances of success in the increasingly conscious market.

However, the use of advanced technology in business coaching is not without its tradeoffs. While it offers efficiency and customization, it also poses risks such as data breaches and loss of human touch. Hence, it's imperative for coaches to strike a balance between the use of technology and traditional methods.

In conclusion, the future of business coaching is filled with exciting possibilities. It is likely to incorporate more technology-based solutions, a greater focus on sustainability, and a personalized approach to meet the entrepreneurs' unique needs. However, the industry must also be prepared to address the challenges that come with these advancements. In a nutshell, the future of business coaching is a brave new world, poised for unprecedented growth and evolution.