The angle of elevation of the top of a tower from a point A due north of it is α and from a point B at a distance of 9 units due west of A is \(\cos^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
If the distance of the point B from the tower is 15 units, then cot α is equal to :
If the distance of the point B from the tower is 15 units, then cot α is equal to :
\(\frac{6}{5}\)
\(\frac{9}{5}\)
\(\frac{4}{3}\)
\(\frac{7}{3}\)
The Correct Option is A
Solution and Explanation
Apply Pythagoras Theorem in NAB,
\(NA = \sqrt{15^2 - 9^2}\)
\(NA=12\)
\(\frac{h}{15} = \tan \theta = \frac{2}{3}\)
\(h = 10\ units\)
\(\cot \alpha = \frac{12}{10}\)
\(\cot \alpha = \frac{6}{5}\)
So, the correct option is (A): \(\frac{6}{5}\)
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Concepts Used:
Distance of a Point From a Line
The length of the perpendicular drawn from the point to the line is the distance of a point from a line. The shortest difference between a point and a line is the distance between them. To move a point on the line it measures the minimum distance or length required.
To Find the Distance Between two points:
The following steps can be used to calculate the distance between two points using the given coordinates:
- A(m1,n1) and B(m2,n2) are the coordinates of the two given points in the coordinate plane.
- The distance formula for the calculation of the distance between the two points is, d = √(m2 - m1)2 + (n2 - n1)2
- Finally, the given solution will be expressed in proper units.
Note: If the two points are in a 3D plane, we can use the 3D distance formula, d = √(m2 - m1)2 + (n2 - n1)2 + (o2 - o1)2.
Read More: Distance Formula
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