If a kite is flying at a height of 60 meters and the angle of elevation from a p
Practice Questions
Q1
If a kite is flying at a height of 60 meters and 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 vertical line?
30 meters
20√3 meters
60 meters
40 meters
Questions & Step-by-Step Solutions
If a kite is flying at a height of 60 meters and 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 vertical line?
Correct Answer: 20√3 meters
Step 1: Understand the problem. We have a kite flying at a height of 60 meters and we need to find the distance from a point on the ground to the base of the kite's vertical line.
Step 2: Identify the angle of elevation. The angle of elevation from the point on the ground to the kite is 60 degrees.
Step 3: Recall the relationship between height, distance, and angle in a right triangle. We can use the tangent function, which is defined as the opposite side (height) over the adjacent side (distance).
Step 4: Write the formula for tangent: tan(angle) = height / distance.
Step 5: Rearrange the formula to find distance: distance = height / tan(angle).
Step 6: Substitute the known values into the formula: distance = 60 / tan(60 degrees).
Step 7: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 8: Substitute tan(60 degrees) into the formula: distance = 60 / √3.
Step 9: Simplify the expression. To make it easier, multiply the numerator and denominator by √3: distance = (60√3) / 3.
Step 10: Calculate the final distance: distance = 20√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 – The scenario can be visualized as a right triangle where the height of the kite is the opposite side, the distance from the point to the base is the adjacent side, and the angle of elevation is the angle between these two sides.
