Question

a 10m high pole is kept vertical by a steel wire .the wire is inclined at an angle of 40° with the horizontal ground.if the wire runs from the top of the pole to the point on the ground where it's other end is fixed , find the length of the wire.​

Answer 1

Given:

A 10m high pole is kept vertical by a steel wire

The wire is inclined at an angle of 40° with the horizontal ground.

If the wire runs from the top of the pole to the point on the ground where it's another end is fixed  

To find:

The length of the wire

Solution:

To solve the given problem we will use the following trigonometric ratios of a triangle:

$\boxed{\bold{sin\:\theta = \frac{Perpendicular}{Hypotenuse} }}$

 

Let's assume,

"AB" → the height of the  vertical pole = 10 m

"AC" → the length of the steel wire

"∠ACB" → the angle of inclination of the steel wire with the horizontal ground = 40°

Here we have,

AB = perpendicular

AC = hypotenuse

θ = 40°

∴  $sin\:\ 40 = \frac{AB}{AC} }}$

$\implies sin\:\ 40 = \frac{10}{AC} }}$

$\implies 0.642 = \frac{10}{AC}$

$\implies AC = \frac{10}{0.642}$

$\implies \bold{AC = 15.57\:m}$

Thus, the length of the steel wire is →  15.57 m.

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Answer 2

Given:

A 10m high pole is kept vertical by a steel wire

The wire is inclined at an angle of 40° with the horizontal ground.

If the wire runs from the top of the pole to the point on the ground where it's another end is fixed  

To find:

The length of the wire

Solution:

To solve the given problem we will use the following trigonometric ratios of a triangle:

$\boxed{\bold{sin\:\theta = \frac{Perpendicular}{Hypotenuse} }}$

 

Let's assume,

"AB" → the height of the  vertical pole = 10 m

"AC" → the length of the steel wire

"∠ACB" → the angle of inclination of the steel wire with the horizontal ground = 40°

Here we have,

AB = perpendicular

AC = hypotenuse

θ = 40°

∴  $sin\:\ 40 = \frac{AB}{AC} }}$

$\implies sin\:\ 40 = \frac{10}{AC} }}$

$\implies 0.642 = \frac{10}{AC}$

$\implies AC = \frac{10}{0.642}$

$\implies \bold{AC = 15.57\:m}$

Thus, the length of the steel wire is →  15.57 m.

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