A kite is flying at a height of 60 meters. If the angle of elevation from a poin
Practice Questions
Q1
A kite is flying at a height of 60 meters. 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?
60√3 meters
30√3 meters
20√3 meters
10√3 meters
Questions & Step-by-Step Solutions
A kite is flying at a height of 60 meters. 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?
Correct Answer: 60√3 meters
Step 1: Understand that the height of the kite is 60 meters.
Step 2: Know that the angle of elevation from the ground to the kite is 30 degrees.
Step 3: Recall that the tangent of an angle in a right triangle is the opposite side (height of the kite) divided by the adjacent side (distance from the point to the base of the kite).
Step 4: Write the formula for distance: Distance = height / tan(angle).
Step 5: Substitute the height (60 meters) and the angle (30 degrees) into the formula.
Step 6: Calculate tan(30 degrees), which is 1/√3.
Step 7: Now, plug this value into the formula: Distance = 60 / (1/√3).
Step 8: Simplify the equation: Distance = 60 * √3.
Step 9: The final answer is that the distance from the point to the base of the kite is 60√3 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the kite to the distance from the point on the ground.
Angle of Elevation – Understanding the concept of angle of elevation is crucial for visualizing the problem and applying the correct trigonometric relationships.
