Triangle

Plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3] give Triangle KLM.

Calculate its area and its interior angles.

Correct result:

S =  103.5
K =  34.966 °
L =  47.6026 °
M =  97.4314 °

Solution:

x0=11 y0=10  x1=10 y1=12  x2=1 y2=3   LM=ML=(k0,k1) k0=x2x1=110=9 k1=y2y1=312=9  KM=MK=(l0,l1) l0=x2x0=111=10 l1=y2y0=3(10)=13  LK=KL=(m0,m1) m0=x0x1=1110=1 m1=y0y1=(10)12=22   k=k02+k12=(9)2+(9)2=9 212.7279 l=l02+l12=(10)2+132=26916.4012 m=m02+m12=12+(22)2=48522.0227  s=k+l+m2=12.7279+16.4012+22.0227225.5759 S=s (sk) (sl) (sm)=25.5759 (25.575912.7279) (25.575916.4012) (25.575922.0227)=2072=10312=103.5
K=angle(KL,KM) K1=arccos(l0 m0l1 m1l m)=arccos((10) 113 (22)16.4012 22.0227)0.6103 K=K1=K1 180π=0.6103 180π=34.966=345758"
L=angle(LK,LM) L1=arccos(k0 m0+k1 m1k m)=arccos((9) 1+(9) (22)12.7279 22.0227)0.8308 L=L1=L1 180π=0.8308 180π=47.603=47.6026=47369"
M1=arccos(k0 l0+k1 l1k l)=arccos((9) (10)+(9) 1312.7279 16.4012)1.7005 M=M1=M1 180π=1.7005 180π=97.431=97.4314=972553"

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Showing 5 comments:
#
Math student
It's Great!. Am grateful.

3 years ago  1 Like
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Still don't get it though

#
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I find it hard ... But I think I will get there. ... Slowly but surely ...

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I still dont understand

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I need one question

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For Basic calculations in analytic geometry is a 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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