A kite is flying at a height of 100 m. 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
1 question
Q1
A kite is flying at a height of 100 m. 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?
100 m
200 m
300 m
400 m
Using tan(30°) = height/distance, we have 1/√3 = 100/distance. Therefore, distance = 100√3 ≈ 173.2 m.
Questions & Step-by-step Solutions
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Q
Q: A kite is flying at a height of 100 m. 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: Using tan(30°) = height/distance, we have 1/√3 = 100/distance. Therefore, distance = 100√3 ≈ 173.2 m.
Steps: 9
Step 1: Understand that the height of the kite is 100 meters.
Step 2: Know that the angle of elevation from the ground to the kite is 30 degrees.
Step 3: Use the tangent function, which relates the angle of elevation to the height and distance from the base of the kite.
Step 4: Write the formula: tan(angle) = height / distance.
Step 5: Substitute the values into the formula: tan(30°) = 100 / distance.
Step 6: Recall that tan(30°) is equal to 1/√3.
Step 7: Set up the equation: 1/√3 = 100 / distance.
Step 8: Rearrange the equation to find distance: distance = 100 * √3.
