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:

n1=(13)2+(35)2=2 22.8284 m2=(16)2+(3n)2 m2=((13)2+(35)2)+(36)2+(5n)2 (16)2+(3n)2=(13)2+(35)2+(36)2+(5n)2 4n=8 n=8/4=2n_{ 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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For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
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See also our trigonometric triangle calculator.

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