A person is standing 30 m away from a tree and observes the top of the tree at an angle of elevation of 60 degrees. What is the height of the tree? (2022)
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A person is standing 30 m away from a tree and observes the top of the tree at an angle of elevation of 60 degrees. What is the height of the tree? (2022)
Q: A person is standing 30 m away from a tree and observes the top of the tree at an angle of elevation of 60 degrees. What is the height of the tree? (2022)
Step 1: Understand the situation. A person is standing 30 meters away from a tree and looking up at the top of the tree.
Step 2: Identify the angle of elevation. The angle at which the person looks up to see the top of the tree is 60 degrees.
Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the tree) divided by the adjacent side (distance from the tree).
Step 4: Set up the equation. We can write the equation as: height = distance * tan(angle). Here, distance is 30 meters and angle is 60 degrees.
Step 5: Calculate tan(60 degrees). The value of tan(60 degrees) is √3 (approximately 1.732).
Step 6: Substitute the values into the equation. Height = 30 * tan(60) = 30 * √3.
