A kite is flying at a height of 50 m. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite? (2021)
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A kite is flying at a height of 50 m. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite? (2021)
Q: A kite is flying at a height of 50 m. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite? (2021)
Step 1: Understand that the kite is flying at a height of 50 meters above the ground.
Step 2: Recognize that the angle of elevation from the point on the ground to the kite is 60 degrees.
Step 3: Recall that the tangent of an angle in a right triangle is the ratio of the opposite side (height of the kite) to the adjacent side (distance from the point to the base of the kite).
Step 4: Set up the equation using the tangent function: tan(60 degrees) = height / distance.
Step 5: Substitute the known values into the equation: tan(60) = 50 / distance.
Step 6: Rearrange the equation to solve for distance: distance = height / tan(60).
Step 7: Calculate tan(60 degrees), which is √3.
Step 8: Substitute tan(60) into the equation: distance = 50 / √3.
Step 9: Simplify the calculation to find the distance: distance ≈ 25 meters.
