A kite is flying at a height of 30 m. If the angle of elevation from a point on
Practice Questions
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
Questions & Step-by-Step Solutions
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?
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.
Step 11: Therefore, the distance from the point on the ground to the base of the kite is 10√3 meters.
Trigonometry – The problem involves using trigonometric ratios, specifically the tangent function, to relate the height of the kite and the distance from the point on the ground.
Angle of Elevation – Understanding the concept of angle of elevation is crucial for visualizing the scenario and applying the correct trigonometric function.
Right Triangle Properties – The scenario can be modeled as a right triangle, where the height of the kite is the opposite side and the distance from the point to the base of the kite is the adjacent side.
