A kite is flying at a height of 30 meters. If the angle of elevation from a poin

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Question: A kite is flying at a height of 30 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:

15√3 meters
30 meters
10√3 meters
20 meters

Correct Answer: 10√3 meters

Solution:

Distance = height / tan(angle) = 30 / √3 = 10√3 meters.

A kite is flying at a height of 30 meters. If the angle of elevation from a poin

Practice Questions

A kite is flying at a height of 30 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?

15√3 meters
30 meters
10√3 meters
20 meters

Questions & Step-by-Step Solutions

A kite is flying at a height of 30 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: 10√3 meters

Step 1: Understand that the height of the kite is 30 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 (30 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: adjacent = 30 / tan(60 degrees).
Step 8: Calculate tan(60 degrees), which is √3.
Step 9: Now substitute tan(60 degrees) into the formula: adjacent = 30 / √3.
Step 10: Simplify the fraction: adjacent = 30 / √3 = 10√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 30 meters. If the angle of elevation from a poin

What’s inside this PDF?

A kite is flying at a height of 30 meters. If the angle of elevation from a poin

Practice Questions

Questions & Step-by-Step Solutions

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