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?
Practice Questions
1 question
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?
Q: 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?
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.
