Answer:
Therefore the value of tangent of ∠[tex]M[/tex] is [tex]42[/tex]°.
Step-by-step explanation:
Given that,
In Δ[tex]MNO[/tex], ∠[tex]O=90[/tex]°, [tex]ON=65,[/tex] [tex]MO=72,[/tex] and [tex]NM=97.[/tex]
and we have to find the value of tangent of ∠[tex]M.[/tex]
Diagram of the given triangle is shown below:
Now,
Δ[tex]MNO[/tex] is a right angle triangle, so we can use all the trigonometric ratio.
[tex]sin\alpha =\frac{Perpendicular}{Hypotenuse}[/tex]
[tex]cos\alpha =\frac{Base}{Hypotenuse}[/tex]
[tex]tan\alpha =\frac{sin\alpha }{cos\alpha }[/tex] = [tex]\frac{Perpendicular}{Base}[/tex]
tangent of ∠[tex]M[/tex] = [tex]\frac{Perpendicular}{Base}[/tex]
= [tex]\frac{ON}{MO}[/tex]
= [tex]\frac{65}{72}[/tex]
= [tex]0.90278[/tex]
∴∠[tex]M[/tex] = [tex]tan^{-1} (0.90278)[/tex]
= [tex]42.0750[/tex]° ≅ [tex]42[/tex]°
Therefore the value of tangent of ∠[tex]M[/tex] is [tex]42[/tex]°.
