A kite is flying at a height of 50 meters. If the angle of elevation from a poin
Practice Questions
Q1
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 60 degrees, how far is the point from the base of the kite?
25√3 meters
50 meters
50√3 meters
75 meters
Questions & Step-by-Step Solutions
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 60 degrees, how far is the point from the base of the kite?
Correct Answer: 25√3 meters
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 60 degrees.
Step 3: Recall the relationship between height, distance, and angle in a right triangle: tan(angle) = opposite/adjacent.
Step 4: In this case, the opposite side is the height of the kite (50 meters) 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: tan(60 degrees) = height / distance.
Step 6: Substitute the known values: tan(60 degrees) = 50 / distance.
Step 7: Know that tan(60 degrees) is equal to √3.
Step 8: Rewrite the equation: √3 = 50 / distance.
Step 9: Rearrange the equation to find distance: distance = 50 / √3.
Step 10: To simplify, multiply the numerator and denominator by √3: distance = (50 * √3) / 3.
Step 11: Calculate the final distance: distance = 25√3 meters.
Trigonometry – The problem involves using trigonometric functions, specifically the tangent function, to relate the height of the kite and the angle of elevation to find the horizontal distance.
Right Triangle Properties – Understanding the properties of right triangles is essential, as the scenario can be visualized as a right triangle where the height is one leg and the distance from the base is the other leg.
