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 30 degrees, how far is the point from the base of the kite?
50√3 meters
25√3 meters
100 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 30 degrees, how far is the point from the base of the kite?
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 30 degrees.
Step 3: Recognize that we can use the tangent function in a right triangle to find the distance from the point on the ground to the base of the kite.
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 distance: distance = height / tan(angle).
Step 7: Substitute the values into the formula: distance = 50 / tan(30 degrees).
Step 8: Know that tan(30 degrees) is equal to 1/√3.
Step 9: Substitute tan(30 degrees) into the formula: distance = 50 / (1/√3).
Step 10: Simplify the equation: distance = 50 * √3.
Step 11: Therefore, the distance from the point on the ground to the base of the kite is 50√3 meters.
Trigonometry – The problem involves using 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 relationship between the sides of a right triangle formed by the height of the kite and the distance from the point on the ground.
