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 °


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"

Try calculation via our triangle calculator.

We would be pleased if you find an error in the word problem or inaccuracies and send it to us. Thank you!

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

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

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

Math student
I still dont understand

Math student
I need one question


Tips to related online calculators
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.
Our vector sum calculator can add two vectors given by its magnitudes and by included angle.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.
Pythagorean theorem is the base for the right triangle calculator.

We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Related math problems and questions:

  • Space vectors 3D
    vectors The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, the distance between the vectors.
  • Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  • Coordinates of square vertices
    ctverec_2 The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square.
  • Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
  • Coordinates of square vertices
    rotate_square I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.
  • Three vectors
    vectors_sum0 The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces.
  • Vector sum
    vectors The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
  • Right triangle
    right_triangles Calculate the missing side b and interior angles, perimeter, and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
  • Angles by cosine law
    357_triangle Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
  • Cuboids
    3dvectors Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
  • Unit vector 2D
    one_1 Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
  • Find the area
    triangles_57 Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft
  • Area and two angles
    trig_1 Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.
  • Four sides of trapezoid
    lichobeznik-stredni_pricka_3 In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
  • Find the 5
    distance-between-point-line Find the equation of the circle with center at (1,20), which touches the line 8x+5y-19=0
  • Find the 10
    lines Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?
  • Airplane navigation
    triangle_airplane An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?