The angle of intersection of AB, BC and AC when, they meet each other at three points, are 54.48°, 81.83° and 43.65°.
What is the law of cosine?
When the three sides of a triangle is known, then to find any angle, the law of cosine is used. It can be given as,
[tex]c^2=a^2+b^2-2ab\cos C\\a^2=c^2+b^2-2ab\cos A\\b^2=a^2+c^2-2ab\cos B[/tex]
Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.
The three straight paths, AB, BC, and AC meet each other at three points, A, B, and C.
- Difference between the points of intersection of A, B and C-
All the points of intersection of given angle A, B and C keeps the different value as all the sides of the triangle is not equal.
- The differences in terms of the angles-
The length of the angle C using the above formula,
[tex]5^2=4.24^2+6.08^2-2(4.24)(6.08)\cos (C)\\C=\cos^{-1}(0.581)\\C=54.48^o[/tex]
Similarly, the measure of angle B,
[tex]6.08^2=5^2+4.24^2-2(5)(4.24)\cos (B)\\B=\cos^{-1}(0.142)\\B=81.83^o[/tex]
The measure of angle A,
[tex]4.24^2=5^2+6.08^2-2(5)(6.08)\cos (A)\\A=\cos^{-1}(0.7235)\\A=43.65^o[/tex]
- The length of the side opposite each angle-
The length of the side opposite to angle A is 4.24 units, side opposite to angle B is 6.08 units and side opposite to angle C is 5 units.
- The pattern regarding the measurements-
All the sides and angles of the triangle are different from each other. This triangle ABC is a scalene triangle.
- Situation in which all the points of intersection resemble one another-
When all the point of intersection of provided line intersect at a single point. Then all the points of intersection resemble one another.
Thus, the angle of intersection of AB, BC and AC when, they meet each other at three points, are 54.48°, 81.83° and 43.65°.
Learn more about the law of cosine here;
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