Question: Two poles of heights 18 metre and 7 metre are erected on a ground. The length of the wire fastened a...

Question

Two poles of heights 18 metre and 7 metre are erected on a ground. The length of the wire fastened at their tops is 22 metre. Find the angle made by the wire with the horizontal?
a. 30
b. 10
c. 20
d. 15

Answer 1

Solution

Hint : Here the question is in the form of word problem. On reading this question we draw a rough diagram related to this question and then the diagram will be related to the plane figures. So by properties of the plane figures further we can solve and get the required answer for the question.

Complete step-by-step answer :

On considering the question we draw a rough diagram.
Here AB and CD represent the pole. The value of AB = 18, CD = 7.
Here we have to determine the value of the angle of elevation.
Let the angle of elevation be x.
Now draw a perpendicular line from point c to the line AB.
Therefore we can say that BE = CD.
The value of AE can be written as
$AE = AB - EB$
On substituting the values we get
$\Rightarrow AE = 18 - 7 = 11$
Therefore the value of AE = 11 m
The triangle is a right angled triangle. by using the concept of trigonometry we can determine the value of angle of elevation.
By the definition of trigonometry ratios we have
$\sin (x) = \dfrac{{opposite}}{{hypotenuse}}$
Here the opposite side of the angle is AE and the hypotenuse side of the angle is AC.
Therefore the sine trigonometry ratio can be written as
$\Rightarrow \sin (x) = \dfrac{{AE}}{{AC}}$
On substituting the values we have
$\Rightarrow \sin (x) = \dfrac{{11}}{{22}}$
On simplifying we have
$\Rightarrow \sin (x) = \dfrac{1}{2}$
The table of sine function for standard angles is given as

Angle	0	30	45	60	90
sin	0	$\dfrac{1}{2}$	$\dfrac{1}{{\sqrt 2 }}$	$\dfrac{{\sqrt 3 }}{2}$	$1$

When we see the table, the value of angle will be
$\Rightarrow x = {30^ \circ }$
Therefore the angle made by the wire with the horizontal is ${30^ \circ }$
Hence option A is the correct one.
So, the correct answer is “Option A”.

Note : Here in this question we can easily guess the plane figure because they have already mentioned the word base and height. In the plane figure of the triangle only we have the word base and height. Suppose if there are other dimensions the plane will be different. For any mathematical problems the basic arithmetic operations are needed.