Find, correct to the nearest degree, the three angles of the triangle with the given vertices.A(1,0,−1),B(4,−3,0),C(1,5,5)∠CAB=?∘∠ABC=?∘∠BCF=?∘∠CAB=?∠ABC=?∠BCA=?

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Gustavo Zimmerman · Accepted Answer

Step 1&amp;nbsp;Find theree angles.Given vertices: АВСА(1,0,−1),В(4,−3,0),С(1,5,5).Distance formula:d=(x2−x1)2+(y2−y1)2+(z2−z1)2Step 2a be the distance between B and C.a=(x2−x1)2+(y2−y1)2+(z2−z102}=(1−4)2+(5−(−3))2+(5−0)2=(−3)2+(8)2+(5)2=(−3)2+(8)2+(5)272Step 3b be the distance between A and C.b=(x2−x1)2+(y2−y1)2+(z2−z12}=(1−1)2+(5−0)2+(5−(−1))2=(0)2+(5)2+(6)2=61Step 4c be the distance between A and B.c=(x2−x1)2+(y2−y1)2+(z2−z12}=(4−1)2+(−3−0)2+(0−(−1))2=(3)2+(−3)2+(1)2=19Step 5Apply cosine law. To get an angle A.cos⁡A=b2+c2−a22bc=(61)2+(19)2−(72)22⋅61⋅19=−0.2644A=cos−1(−0.2644)A=105.33∘

lamontalbanav6 · Accepted Answer

Step 6Apply cosine law. To get an angle B.cos⁡B=b2+c2−a22bc=(72)2+(19)2−(61)22⋅72⋅19=0.6489A=cos−1(0.6489)A=49.54∘

Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A (1, 0,-1), B (4, -3,0), C (1, 5 ,5), ∠ CAB= ^o, ∠ABC= ^o, ∠ BCF= ^o, ∠CAB = ?, ∠ABC = ?, ∠BCA = ?

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