Answer
Verified
334.7k+ views
Hint: Draw a diagram of the given situation and use sine of the angles given, to determine the distance of the bird from the girl. The diagram of the situation mainly consists of right angle triangles.
Complete step-by-step answer:
The angle of elevation is the angle between the horizontal line of sight and the line of sight up to an object. For example, if we are standing on the ground and looking at the top of a tower then the angle subtended between the horizontal line and the line of sight is called angle of elevation.
Now, we come to the question. Let us assume that the boy is standing at point B, girl at G and bird is at point A. The tower on which the girl is standing is GN, where N is the base of the tower. We know that, $\sin \theta =\dfrac{perpendicular}{Hypotenuse}$.
In triangle ABM,
$\begin{align}
& \sin {{30}^{\circ }}=\dfrac{AM}{AB} \\
& \dfrac{1}{2}=\dfrac{AM}{100} \\
& \therefore AM=50\text{ m} \\
\end{align}$
Now, $GN=OM=20\text{ m}$, where GN is the height of the tower and OM is the side opposite to GN in the rectangle OMNG. Therefore, the length of $AO$$=AM-OM=50-20=30\text{ m}$.
In triangle AOG,
$\begin{align}
& \sin {{45}^{\circ }}=\dfrac{AO}{AG} \\
& \dfrac{1}{\sqrt{2}}=\dfrac{30}{AG} \\
& \therefore AG=30\sqrt{2}\text{ m} \\
\end{align}$
Hence, distance of the girl from the bird $=AG=30\sqrt{2}\text{ m}$.
Note: It is important to draw the diagram of the given situation because diagrams will help us to solve the question more easily as compared to just imagining and solving. Also, sine of the angle is used because we had to find the hypotenuse of the right angle triangle and the length of perpendicular was given to us.
Complete step-by-step answer:
The angle of elevation is the angle between the horizontal line of sight and the line of sight up to an object. For example, if we are standing on the ground and looking at the top of a tower then the angle subtended between the horizontal line and the line of sight is called angle of elevation.
Now, we come to the question. Let us assume that the boy is standing at point B, girl at G and bird is at point A. The tower on which the girl is standing is GN, where N is the base of the tower. We know that, $\sin \theta =\dfrac{perpendicular}{Hypotenuse}$.
In triangle ABM,
$\begin{align}
& \sin {{30}^{\circ }}=\dfrac{AM}{AB} \\
& \dfrac{1}{2}=\dfrac{AM}{100} \\
& \therefore AM=50\text{ m} \\
\end{align}$
Now, $GN=OM=20\text{ m}$, where GN is the height of the tower and OM is the side opposite to GN in the rectangle OMNG. Therefore, the length of $AO$$=AM-OM=50-20=30\text{ m}$.
In triangle AOG,
$\begin{align}
& \sin {{45}^{\circ }}=\dfrac{AO}{AG} \\
& \dfrac{1}{\sqrt{2}}=\dfrac{30}{AG} \\
& \therefore AG=30\sqrt{2}\text{ m} \\
\end{align}$
Hence, distance of the girl from the bird $=AG=30\sqrt{2}\text{ m}$.
Note: It is important to draw the diagram of the given situation because diagrams will help us to solve the question more easily as compared to just imagining and solving. Also, sine of the angle is used because we had to find the hypotenuse of the right angle triangle and the length of perpendicular was given to us.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE