Question

A household subtends a right angle at the window of an opposite house and the angle of elevation of the window from the bottom of the first house is \[{60^ \circ }\]. If the distance between the two houses is\[6m\] , then the height of the first house is
A.\[8\sqrt 3 m\]
B.\[6\sqrt 3 m\]
C.\[4\sqrt 3 m\]
D.None of these

Answer 1

Hint: The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

Complete answer:
Construct the diagram with the help of given information.
The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
The three terms related to the angle of elevation are
1.Angle
2.Horizontal Line
3.Line of sight
Angle: If two rays or two line segments meet at a common endpoint, then the point is known as the vertex. Two straight lines meeting at a common point is said to form an angle.
Horizontal Line: A straight line on the coordinate flat surface where all points on the line have the same y-coordinate. The angle and horizontal line combine to form the angle of elevation.
Line of Sight: The line which is drawn from the eyes of the observer to the point being viewed on the object is known as the line of sight.

In \[\Delta ADC\]
\[\dfrac{{AD}}{{AB}} = \tan {60^ \circ }\]
\[\dfrac{{AD}}{6} = \sqrt 3 \]
Therefore \[AD = 6\sqrt 3 \]
In \[\Delta DEC\]
\[\dfrac{{DC}}{{EC}} = \tan {60^ \circ }\]
\[\dfrac{6}{{EC}} = \sqrt 3 \]
Therefore \[EC = 2\sqrt 3 \]
Therefore we get \[h = EC + CB\]
\[h = 2\sqrt 3 + 6\sqrt 3 = 8\sqrt 3 \]
Therefore the height of the first house is \[8\sqrt 3 m\].
Hence , the correct option is A .

Note:
The formula for finding the angle of elevation depends on knowing the information such as the measures of the opposite, hypotenuse, and adjacent side to the right angle. If the distance from the object and height of the object is given, then the formula for the angle of elevation is given by
Tangent of the angle of elevation \[ = \dfrac{{height\,of\,the\,object}}{{dis\tan ce\,from\,the\,object}}\]