Answer:
The Length of MN is 15.6 cm.
Step-by-step explanation:
Given:
A right angled triangle LMN at angle M is equal to 90°
LN = Hypotenuse = 16.9 cm
LM = Shorter leg = 6.5 cm
To Find:
MN = Longer leg = ?
Solution:
In Right Angled Triangle Δ LMN
Pythagoras Theorem States that
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
By applying Pythagoras theorem we get
[tex]l(LN)^{2}= l(LM)^{2}+l(MN)^{2} \\\textrm{substituting the given values of we get}\\\\16.9^{2}= 6.5^{2}+ (MN)^{2}\\ \therefore (MN)^{2}=285.61-42.25\\l(MN)^{2}=243.36\\l(MN)=\pm \sqrt{243.36}\\l(MN)=15.6\ cm .........\textrm{as distance cannot be in negative}[/tex]
The Length of MN is 15.6 cm.
