Answer
Verified
390k+ views
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
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.
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.
Recently Updated Pages
Who among the following was the religious guru of class 7 social science CBSE
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Trending doubts
A rainbow has circular shape because A The earth is class 11 physics CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE