# Right angled triangle 2

LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n

Result

n =  2

#### Solution:

$n_{ 1 } = \sqrt{ (1-3)^2+(3-5)^2 } = 2 \ \sqrt{ 2 } \doteq 2.8284 \ \\ m^2 = (1-6)^2 + (3-n)^2 \ \\ m^2 = ((1-3)^2+(3-5)^2) + (3-6)^2 + (5-n)^2 \ \\ (1-6)^2 + (3-n)^2 = (1-3)^2+(3-5)^2 + (3-6)^2 + (5-n)^2 \ \\ 4n = 8 \ \\ n = 8/4 = 2$

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