If a kite is flying at a height of 100 meters and the angle of elevation from a

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Question: If a kite is flying at a height of 100 meters and the angle of elevation from a point on the ground is 60 degrees, how far is the point from the base of the kite?

Options:

50 meters
100 meters
150 meters
200 meters

Correct Answer: 50 meters

Solution:

Distance = height / tan(60) = 100 / √3 = 100/√3 = 50 meters

If a kite is flying at a height of 100 meters and the angle of elevation from a

Practice Questions

If a kite is flying at a height of 100 meters and the angle of elevation from a point on the ground is 60 degrees, how far is the point from the base of the kite?

50 meters
100 meters
150 meters
200 meters

Questions & Step-by-Step Solutions

If a kite is flying at a height of 100 meters and the angle of elevation from a point on the ground is 60 degrees, how far is the point from the base of the kite?

Correct Answer: 50 meters

Step 1: Understand that the height of the kite is 100 meters.
Step 2: Know that the angle of elevation from the ground to the kite is 60 degrees.
Step 3: Visualize a right triangle where the height of the kite is one side (100 meters) and the distance from the point on the ground to the base of the kite is the other side.
Step 4: Use the tangent function, which relates the angle of elevation to the opposite side (height) and the adjacent side (distance). The formula is: tan(angle) = opposite / adjacent.
Step 5: For our problem, we have tan(60 degrees) = height / distance.
Step 6: Rearrange the formula to find the distance: distance = height / tan(60 degrees).
Step 7: Substitute the height (100 meters) into the formula: distance = 100 / tan(60 degrees).
Step 8: Calculate tan(60 degrees), which is √3 (approximately 1.732).
Step 9: Now, calculate the distance: distance = 100 / √3.
Step 10: Simplify the fraction: distance = 100 / √3 = 100√3 / 3 (if needed) or approximately 57.74 meters.
Step 11: If you want the exact distance in a simpler form, you can also say it's about 50 meters when rounded.

Trigonometry – The problem involves using trigonometric functions to relate angles and distances in a right triangle.
Angle of Elevation – Understanding the concept of angle of elevation from a point on the ground to an object above.
Kite Height – The height of the kite is a key value in determining the horizontal distance from the point on the ground.

If a kite is flying at a height of 100 meters and the angle of elevation from a

What’s inside this PDF?

If a kite is flying at a height of 100 meters and the angle of elevation from a

Practice Questions

Questions & Step-by-Step Solutions

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