the vertices of ABC are points A(1,1), B(4,1), and C(4,5). find the cosines of the angles of the triangle.
2 answers:
Answer:
- cos(A) = 3/5
- cos(B) = 0
- cos(C) = 4/5
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between the cosine of an angle and the sides of the triangle.
Cos = Adjacent/Hypotenuse
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<h3>Angle A</h3>In the given triangle, the hypotenuse is AC. The side adjacent to angle A is AB, so its cosine is ...
cos(A) = AB/AC
cos(A) = 3/5
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<h3>Angle B</h3>The right angle in the triangle is angle B. The cosine of a right angle is 0.
cos(B) = 0
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<h3>Angle C</h3>The side adjacent to angle C is CB, so its cosine is ...
cos(C) = CB/AC
cos(C) = 4/5
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The solutions to the systems of equations are:
1. (2, 3) (see attachment below). [one solution]
2. no solution
3. (3, 13) [one solution]
<h3>Solution to a System of Equations?</h3>The solution to a system of equations is the x-value and y-value that will make both equations true. It can be found either using a graph, by elimination method, or substitution method as explained below.
1. Using graph to solve y = 2x - 1 and y = 4x - 5:
The solution is the point where both lines intersect which is: (2, 3) (see attachment below). [one solution]
2. Solving using substitution method:
x = -5y + 4 ---> eqn. 1
3x + 15y = -1 ---> eqn. 2
Substitute x = -5y + 4 into eqn. 2
3(-5y + 4) + 15y = -1
-15y + 12 + 15y = -1
-15y + 15y = -1 - 12
0 = -13 (this shows that there is no solution)
3. Using elimination method:
14x = 2y + 16 ---> eqn. 1
5x = y + 2 ---> eqn. 2
1(14x = 2y + 16)
2(5x = y + 2)
14x = 2y + 16 ----> eqn. 3
10x = 2y + 4 -----> eqn. 4
Subtract
4x = 12
x = 12/4
x = 3
Substitute x = 3 into eqn. 2
5(3) = y + 2
15 = y + 2
15 - 2 = y
13 = y
y = 13
The solution is: (3, 13).
Learn more about the solution of a system of equations on:
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