Question

Look at the figure below.

Answer 1

Answer:

∴ $\tan \theta = -\frac{3}{4}$

Step-by-step explanation:

Let the triangle  name as Δ ABO a right  triangle at ∠ B =90°

Such that,

OA = radius

AB = y coordinate = 12

BO = x coordinate = 16  (positive because distance cannot be in negative)

To Find:

$\tan \theta=?$

Solution:

In right  triangle Δ ABO ,By Pythagoras theorem we get the radius,

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

$r^{2} = 16^{2}+12^{2}\\\\r^{2} =400\\\therefore r = 20\ units$

∴ OA = 20

   OB = 16

Also tan (180 -θ) = - tan (θ)

Now In right  triangle Δ ABO

m∠ AOB = 180 -θ

∴ $\tan (\angle AOB) = \frac{\textrm{side opposite to angle AOB}}{\textrm{side adjacent to angle AOB}}\\\\\tan (180 -\theta) = \frac{AB}{OB}\\\\-\tan \theta =\frac{12}{16} \\\\\tan \theta = -\frac{3}{4}$

∴ $\tan \theta = -\frac{3}{4}$