You are given five points

A= [ 15 25 60];

B= [-10 5 20];

C=[ 14 30 10]

D=[30 -18 12];

E=[ 17 20 111];

Use the following to create the shape.

Answer the following questions. Please give answers where specified ( ANSWER).

Question 1

Part A

Point A is the top of the tetrahedron. The Triangles CAB, DBA, and DCA all meet there. Find the three vertex angles at A. Leave the angles in Radians( note that all three angles should be acute and their sum is

Angle 1= ANSWER (Radians) Angle 2 = Answer (radians) Angle 3 = Answer(radians)

Part B

Find the total surface area of the tetrahedron, all four angles.

Total Area = (square units) ANSWER

27 34 First, create corner points for irregular tetrahedron A 15 25 60 B [-10 5 20 C [14 30 101 D [30 18 12] Second, organize the X, Y, 2 columns for a triangle patch Joe [A: B: C] Sam [A: B: D] Hank [A: C: D1 Mike [C:B: D] Third, display the patches and make the tetrahedron PJoe patch (Joe 1), Joe 2) Joe 3) 'g') PSam patch (Sam 1), Sam 2) r Sam 3) 'r') PHank patch (Hank 1), Hank 2), Hank 3) y'); PMike patch (Mike 1) ,Mike 2) ,Mike 3) 'b') s Polish up the display grid. xlabel ('x'), ylabel ('Y'), zlabel z') view (-80,25) axis (I-20 500 20 50 0 1151) daspect (11 1 11) hold on create and display a fifth point, up above the tetrahedron s DirCA (A-C) orm (A-C) E A (norm (A-C) DirCA) E (3) 111: scatter 3 (E (1) E (2) E (3), 35 'k', create and display a sixth point, no far from side "Sam", or ABD centroid. (A+B+D) /3 just to have a starting point UN, MAGI Unit Normal F (A, B, D) 3 call on home made function create a new point normal t the centroid. F centroid. 30 UNW s F 1237 6018 47.9319 by raw calculation rounding the numbers for easy communication to the class 18 481 scatter3 (F (1) F (2), F (3), 350 5755 tUNV -0.3181 0. 7S34 dar (UNV, A) 10.924208127322 256 27 34 First, create corner points for irregular tetrahedron A 15 25 60 B [-10 5 20 C [14 30 101 D [30 18 12] Second, organize the X, Y, 2 columns for a triangle patch Joe [A: B: C] Sam [A: B: D] Hank [A: C: D1 Mike [C:B: D] Third, display the patches and make the tetrahedron PJoe patch (Joe 1), Joe 2) Joe 3) 'g') PSam patch (Sam 1), Sam 2) r Sam 3) 'r') PHank patch (Hank 1), Hank 2), Hank 3) y'); PMike patch (Mike 1) ,Mike 2) ,Mike 3) 'b') s Polish up the display grid. xlabel ('x'), ylabel ('Y'), zlabel z') view (-80,25) axis (I-20 500 20 50 0 1151) daspect (11 1 11) hold on create and display a fifth point, up above the tetrahedron s DirCA (A-C) orm (A-C) E A (norm (A-C) DirCA) E (3) 111: scatter 3 (E (1) E (2) E (3), 35 'k', create and display a sixth point, no far from side "Sam", or ABD centroid. (A+B+D) /3 just to have a starting point UN, MAGI Unit Normal F (A, B, D) 3 call on home made function create a new point normal t the centroid. F centroid. 30 UNW s F 1237 6018 47.9319 by raw calculation rounding the numbers for easy communication to the class 18 481 scatter3 (F (1) F (2), F (3), 350 5755 tUNV -0.3181 0. 7S34 dar (UNV, A) 10.924208127322 256