Answer :
Final Answer
The angle of elevation of the sun is approximately 60 degrees.
Explanation
To find the angle of elevation, we use the concept of trigonometry. The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. In this scenario, the pole forms the opposite side, the shadow forms the adjacent side, and the angle of elevation is the angle we want to find.
Given that the shadow of the pole is 3 times its height (3h), we can set up the equation:
tan(θ) = h / (3h)
Simplifying the equation, we get:
tan(θ) = 1/3
Taking the arctan of both sides to find the angle, we get:
θ ≈ 60 degrees
Trigonometry plays a crucial role in solving problems related to heights and distances. It's a branch of mathematics that deals with the relationships between the sides and angles of triangles. In this scenario, we used the tangent function, which is just one of the trigonometric functions alongside sine and cosine. Understanding these functions allows us to work with angles and lengths in various practical situations, from surveying land to calculating distances in physics problems. This application showcases the real-world relevance of trigonometry in solving everyday problems.
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