Question

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 :

• A. $\frac{6}{5}$
• B. $\frac{9}{5}$
• C. $\frac{4}{3}$
• D. $\frac{7}{3}$

Answer 1

Answer: (A)

$\frac{6}{5}$

Answer 2

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): $\frac{6}{5}$