The tops of two poles of height 16m and 10m are connected by a wire of length l metres. If the wire makes an angle of 30° with the horizontal, then l =
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We are given:
Height of the first pole = 16 m,
Height of the second pole = 10 m,
The wire makes an angle of 30° with the horizontal.
Find the vertical difference between the tops of the poles
The vertical difference between the tops of the two poles is:
16 – 10 = 6 m.
Step 2: Use the sine function
The wire forms the hypotenuse of a right triangle, where:
The vertical difference (6 m) is the opposite side,
The angle between the wire and the horizontal is 30°.
Using the sine function:
sinθ = (Opposite side) / (Hypotenuse).
Substitute the values:
sin30° = 6 / l.
From trigonometric values, sin30° = 1/2:
1/2 = 6 / l.
Solve for l
Multiply through by l:
l × (1/2) = 6.
Simplify:
l = 6 × 2 = 12 m
This question related to Chapter 9 Mathematics Class 10th NCERT. From the Chapter 9 Applications of Trigonometry. Give answer according to your understanding.
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