A kite is flying at a height of 100 meters. If the angle of depression from the
Practice Questions
Q1
A kite is flying at a height of 100 meters. If the angle of depression from the kite to a point on the ground is 30 degrees, how far is the point from the point directly below the kite?
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Questions & Step-by-Step Solutions
A kite is flying at a height of 100 meters. If the angle of depression from the kite to a point on the ground is 30 degrees, how far is the point from the point directly below the kite?
Step 1: Understand that the kite is flying at a height of 100 meters above the ground.
Step 2: Recognize that the angle of depression from the kite to a point on the ground is 30 degrees.
Step 3: Visualize a right triangle where the height of the kite (100 meters) is one side (the opposite side) and the distance from the point directly below the kite to the point on the ground is the other side (the adjacent side).
Step 4: Use the tangent function, which relates the angle to the opposite and adjacent sides of a right triangle. The formula is tan(angle) = opposite/adjacent.
Step 5: Substitute the known values into the formula: tan(30°) = 100/distance.
Step 6: Know that tan(30°) equals 1/√3.
Step 7: Set up the equation: 1/√3 = 100/distance.
Step 8: Rearrange the equation to solve for distance: distance = 100 * √3.
Step 10: Final calculation gives distance ≈ 173.21 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the kite and the angle of depression to find the horizontal distance.
Angle of Depression – Understanding the angle of depression from the kite to the ground point is crucial for setting up the correct trigonometric relationship.
