A kite is flying at a height of 30 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?
Practice Questions
1 question
Q1
A kite is flying at a height of 30 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?
15√3 m
30 m
10√3 m
20 m
Using tan(60°) = height/distance, we have distance = height/tan(60°) = 30/√3 = 15√3 m.
Questions & Step-by-step Solutions
1 item
Q
Q: A kite is flying at a height of 30 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?
Solution: Using tan(60°) = height/distance, we have distance = height/tan(60°) = 30/√3 = 15√3 m.
Steps: 11
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 in a right triangle: tan(angle) = opposite side / adjacent side.
Step 4: In this case, the opposite side is the height of the kite (30 m) 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 using the tangent function: tan(60°) = height / distance.
Step 6: Substitute the known values into the equation: tan(60°) = 30 / distance.
Step 7: Calculate tan(60°), which is √3.
Step 8: Rewrite the equation: √3 = 30 / distance.
Step 9: Rearrange the equation to find distance: distance = 30 / √3.
