A kite is flying at a height of 50 meters. If the angle of elevation from a point on the ground is 30 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 is 30 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 is 30 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 point on the ground to the kite is 30 degrees.
Step 3: Recall that the tangent of an angle in a right triangle is the opposite side (height of the kite) divided by the adjacent side (distance from the point to the base of the kite).
Step 4: Write the formula for tangent: tan(angle) = opposite / adjacent.
Step 5: Substitute the known values into the formula: tan(30 degrees) = height / distance.
Step 6: Rearrange the formula to find distance: distance = height / tan(30 degrees).
Step 7: Calculate tan(30 degrees), which is 1/√3.
Step 8: Substitute the height (50 meters) and tan(30 degrees) into the formula: distance = 50 / (1/√3).
Step 9: Simplify the calculation: distance = 50 * √3.
Step 10: Conclude that the distance from the point to the base of the kite is 50√3 meters.
