Question

In triangle LMN, if LM = 10 cm and angle LNM = 90 degree, angle LMN = 30 degree; then NM = ?

Answer 1

here is your answer....

Answer 2

Given,

In a ΔLMN,

LM = 10 cm,

∠LNM = 90°, and,

∠LMN = 30°.

To find,

NM

Solution,

We can solve this problem simply by following the below process.

Here, it is given that in ΔLMN, ∠LNM = 90°. So, LM will be the hypotenuse. LM is given as 10 cm.

Now, to find the NM, which is the base of ΔLMN, we can apply the trigonometric function, which relates the base and hypotenuse of a right triangle, that is $cos\theta$, by taking ∠LMN as $\theta$.

Now, since

$cos\theta=\frac{base}{hypotenuse}$

Here, for the given problem,

$cos30=\frac{NM}{LM}$

⇒ $NM=LM\cdot cos30$

⇒ $NM = 10\cdot \frac{\sqrt{3}}{2}$

⇒ $NM = 5\sqrt{3} .$

Therefore, for the given triangle LMN, the value of NM will be 5√3.