In the figure given below, AD=4cm,BD=3cm and CB=12 cm, then cotƟ equals
(a) 3/4
(b) 5/12
(c) 4/3
(d) 12/5
(d) `12/5`
Explanation:
First we need to find AB,
By Pythagoras theorem
`"AB"^{2}`=`"AD"^{2}`+`"BD"^{2}`
=`"AB"^{2}`=`"4"^{2}`+`"3"^{2}`
=`"AB"^{2}`= 16 + 9
=`"AB"^{2}`= 16 + 9
=`"AB"^{2}`= 25
=`"AB"^{2}`= `"5"^{2}`
∴ AB = 5
Now,
tan θ = `"AB"/"BC"`
tan θ = `"5"/"12"`
So,
cot θ = `12/5`
So, the correct answer is option (d) 12/5