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A kite is flying in the sky. A person is holding the kite with 40 m long tightly stretched string. Find the height of the kite (in meters) if the angle made by the string with the horizontal is 30 degrees.
20
30
15
10
30
In a 30-60-90 triangle, the sides are in the ratio 1: 3тАЛ: 2. Since the hypotenuse (2 units) is 40 m, the side opposite 30 degrees (1 unit) must be 40 / 2 = 20 m.
Length of the string (hypotenuse) l = 40 m, angle of elevation (theta) = 30 degrees.
sin(╬╕)=HypotenuseHeightтАЛ
In a 30-60-90 triangle, the sides are in the ratio 1: 3тАЛ: 2. Since the hypotenuse (2 units) is 40 m, the side opposite 30 degrees (1 unit) must be 40 / 2 = 20 m.
Students often confuse the sine ratio (opposite/hypotenuse) with the cosine ratio (adjacent/hypotenuse) or incorrectly identify the string as the height rather than the hypotenuse.
Identify the Triangle Components
Represent the situation as a right-angled triangle where the string is the hypotenuse, the height of the kite is the opposite side, and the angle is 30 degrees.
Hypotenuse=40,╬╕=30┬░
Apply Sine Ratio
Use the definition of sine for the angle of elevation: sin(30┬░)=HypotenuseHeightтАЛ.
sin(30┬░)=40hтАЛ
Calculate the Result
Substitute the value of sin(30┬░)=0.5 into the equation and solve for h.
h=40├Ч0.5=20┬аm
A is correct because the calculation based on the trigonometric ratio sin(30┬░)=h/40 yields a height of 20 m.
This concept is fundamental to Height and Distance problems; mastering the 1: 3тАЛ: 2 ratio for 30-60-90 triangles will save significant time in competitive exams.
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