Answer :
Final answer:
Using the tangent function and the height of the tree along with the horizontal distance, we calculated that the angle of elevation to the top of the tree is approximately 73.1 degrees. This demonstrates the basic principles of trigonometry in a real-world application. Understanding how to use the tangent function helps in solving similar problems involving heights and distances.
Explanation:
Finding the Angle of Elevation to a Tree
To determine the angle of elevation from a point 57 feet away from a tree with a height of 186 feet, we can use basic trigonometry. This involves the concept of the right triangle where:
- The height of the tree (rise) = 186 feet
- The horizontal distance from the base of the tree (run) = 57 feet
We will use the tangent function, which is defined as:
tan(θ) = (height of the tree) / (horizontal distance)
Plugging the values into the equation:
tan(θ) = 186 feet / 57 feet
Calculating this gives:
tan(θ) = 3.2632
To find the angle θ, we will use the arctangent function:
θ = arctan(3.2632)
Using a calculator, we find:
θ ≈ 73.1 degrees
Thus, the angle of elevation from the point 57 feet away to the top of the tree is approximately 73.1 degrees, rounded to the nearest tenth.
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