Answer :
Final answer:
The height of the tree can be calculated using trigonometry and the given angle of elevation. We set up a right triangle and use the tangent of 53.4°, which is equal to the height of the tree divided by 39.3 ft, and solve for the tree's height.
Explanation:
The question refers to an application of trigonometry in solving real-world problems, specifically using angles of elevation.
We can visualize the given problem as a right triangle, where the base is the distance from the point to the base of the tree (39.3 ft), the height is the tree's height which we need to find, and the angle of elevation is given as 53.4°.
From trigonometry, we know that the tangent of an angle in a right triangle is the ratio of the side opposite to the angle (the height of the tree in this case) to the side adjacent to the angle (the distance from the point to the tree). So, we have:
Tan(53.4°) = Height of tree / 39.3 ft
Solving for the Height of tree gives us:
Height of tree = Tan(53.4°) * 39.3 ft
Use a calculator to compute this and you'll find the height of the tree.
Learn more about Trigonometry here:
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