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's height?
25 meters
30 meters
35 meters
40 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's height?
Correct Answer: 28.87 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: Recognize that we can use the tangent function to find the distance from the point on the ground to the base of the kite's height.
Step 4: Recall the formula for tangent: tan(angle) = opposite / adjacent.
Step 5: In this case, the 'opposite' side is the height of the kite (50 meters) and the 'adjacent' side is the distance we want to find.
Step 6: Rearrange the formula to find the adjacent side: adjacent = opposite / tan(angle).
Step 7: Substitute the values into the formula: adjacent = 50 / tan(60 degrees).
Step 8: Calculate tan(60 degrees), which is √3 (approximately 1.732).
Step 9: Now substitute this value into the formula: adjacent = 50 / √3.
Step 10: Perform the division: 50 / 1.732 = approximately 28.87 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.
