Question

In ΔMNO, the measure of ∠O=90°, ON = 65, MO = 72, and NM = 97. What is the value of the tangent of ∠M to the nearest hundredth?

Answer 1

Answer:

Therefore the value of tangent of ∠$M$ is $42$°.

Step-by-step explanation:

Given that,

                  In Δ$MNO$, ∠$O=90$°, $ON=65,$ $MO=72,$ and $NM=97.$

and we have to find the value of tangent of ∠$M.$

Diagram of the given triangle is shown below:

Now,

Δ$MNO$ is a right angle triangle, so we can use all the trigonometric ratio.

$sin\alpha =\frac{Perpendicular}{Hypotenuse}$

$cos\alpha =\frac{Base}{Hypotenuse}$

$tan\alpha =\frac{sin\alpha }{cos\alpha }$ = $\frac{Perpendicular}{Base}$

tangent of ∠$M$ = $\frac{Perpendicular}{Base}$

                         = $\frac{ON}{MO}$

                         = $\frac{65}{72}$

                         = $0.90278$

∴∠$M$ = $tan^{-1} (0.90278)$

        = $42.0750$° ≅ $42$°

Therefore the value of tangent of ∠$M$ is $42$°.