A kite is flying at a height of 30 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's height?

Practice Questions

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15√3 meters
30 meters
20 meters
10√3 meters

Questions & Step-by-step Solutions

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Q: A kite is flying at a height of 30 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's height?

Solution: Distance = height / tan(angle) = 30 / (√3/3) = 30√3/3 = 10√3 meters.

Steps: 9

Step 1: Understand that the height of the kite is 30 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: height = distance * tan(angle).
Step 4: Rearrange the formula to find distance: distance = height / tan(angle).
Step 5: Substitute the height (30 meters) and the angle (60 degrees) into the formula.
Step 6: Calculate tan(60 degrees), which is √3.
Step 7: Substitute tan(60 degrees) into the formula: distance = 30 / (√3).
Step 8: To simplify, multiply the numerator and denominator by √3: distance = 30√3 / 3.
Step 9: Simplify the fraction: distance = 10√3 meters.

A kite is flying at a height of 30 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's height?

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