A Farmer Plans to Build a Triangular Fence with Side Lengths of 500 m, 461 m, and 408 m. What Are the Measures of the Angles?
The Law of Cosines states that in a triangle with sides of length a, b, and c and opposite angles A, B, and C, the following equation holds:
c^2 = a^2 + b^2 - 2ab cos(C)
Using this law, we can solve for the angles of the triangle. Let's label the sides as follows:
a = 500 m
b = 461 m
c = 408 m
We can use the Law of Cosines to solve for the angle C opposite side c:
408^2 = 500^2 + 461^2 - 2(500)(461) cos(C)
Solving for C, we get:
C = 104.4 degrees
We can then use the Law of Sines to solve for the other angles:
sin(A)/a = sin(C)/c
Solving for A, we get:
A = 42.8 degrees
Similarly, we can solve for B:
B = 32.8 degrees
Therefore, the measures of the angles of the triangle are:
- Angle A: 42.8 degrees
- Angle B: 32.8 degrees
- Angle C: 104.4 degrees
Related Questions
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- What is the length of the longest side of the triangle?
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