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 30 degrees, how far is the point from the base of the kite?

Practice Questions

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50√3 meters
25√3 meters
100 meters
75 meters

Questions & Step-by-step Solutions

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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 30 degrees, how far is the point from the base of the kite?

Solution: Distance = height / tan(angle) = 50 / (1/√3) = 50√3 meters.

Steps: 11

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 30 degrees.
Step 3: Recognize that we can use the tangent function in a right triangle to find the distance from the point on the ground to the base of the kite.
Step 4: Recall the formula for tangent: tan(angle) = opposite / adjacent.
Step 5: In this case, the opposite side is the height of the kite (50 meters) and the adjacent side is the distance we want to find.
Step 6: Rearrange the formula to find the distance: distance = height / tan(angle).
Step 7: Substitute the values into the formula: distance = 50 / tan(30 degrees).
Step 8: Know that tan(30 degrees) is equal to 1/√3.
Step 9: Substitute tan(30 degrees) into the formula: distance = 50 / (1/√3).
Step 10: Simplify the equation: distance = 50 * √3.
Step 11: Therefore, the distance from the point on the ground to the base of the kite is 50√3 meters.

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 30 degrees, how far is the point from the base of the kite?

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