A kite is flying at a height of 50 meters. 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?
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A kite is flying at a height of 50 meters. 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?
Q: A kite is flying at a height of 50 meters. 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?
Step 1: Understand that the height of the kite is 50 meters.
Step 2: Know that the angle of elevation from the ground to the kite is 60 degrees.
Step 3: Recall the relationship between height, distance, and angle in a right triangle: tan(angle) = opposite/adjacent.
Step 4: In this case, the opposite side is the height of the kite (50 meters) and the adjacent side is the distance from the point on the ground to the base of the kite.
Step 5: Set up the equation: tan(60 degrees) = height / distance.
Step 6: Substitute the known values: tan(60 degrees) = 50 / distance.
Step 7: Know that tan(60 degrees) is equal to √3.
Step 8: Rewrite the equation: √3 = 50 / distance.
Step 9: Rearrange the equation to find distance: distance = 50 / √3.
Step 10: To simplify, multiply the numerator and denominator by √3: distance = (50 * √3) / 3.
Step 11: Calculate the final distance: distance = 25√3 meters.
