A kite is flying at a height of 100 meters. If the angle of elevation from a poi

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Question: A kite is flying at a height of 100 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?

Options:

50 meters
100 meters
150 meters
200 meters

Correct Answer: 50 meters

Solution:

Distance = height / tan(angle) = 100 / √3 = 100√3/3 meters.

A kite is flying at a height of 100 meters. If the angle of elevation from a poi

Practice Questions

A kite is flying at a height of 100 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?

50 meters
100 meters
150 meters
200 meters

Questions & Step-by-Step Solutions

A kite is flying at a height of 100 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?

Correct Answer: 57.74 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: Recognize that we can use the tangent function 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 (100 meters) and the adjacent side is the distance we want to find.
Step 6: Rearrange the formula to find the distance: adjacent = opposite / tan(angle).
Step 7: Substitute the values into the formula: distance = 100 / tan(60 degrees).
Step 8: Know that tan(60 degrees) is √3.
Step 9: Calculate the distance: distance = 100 / √3.
Step 10: Simplify the answer: distance = 100√3 / 3 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.

A kite is flying at a height of 100 meters. If the angle of elevation from a poi

What’s inside this PDF?

A kite is flying at a height of 100 meters. If the angle of elevation from a poi

Practice Questions

Questions & Step-by-Step Solutions

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