Tom, Aaron, and Harry are camping in their tents. If the distance between Tom and Aaron is 153 feet, the distance between Tom an
d Harry is 201 feet, and the distance between Aaron and Harry is 175 feet, what is the angle between Aaron, Harry, and Tom?
1 answer:
Answer: The angles between Aaron, Harry, and Tom are 57.32, 74.75 and 47.93 degrees
Step-by-step explanation:
The triangle ABC formed as a result of their positions is shown in the attached photo. We will apply the cosine rule. It states that
a^2 = b^2 + c^2 - 2bcCosA
From the diagram,
a = 175 feet
b = 201 feet
c = 153 feet
175^2 = 201^2 + 153^2 - 2×201×153Cos A
30625 = 40401 + 23409 - 61506CosA
30625 = 63810 - 61506CosA
61506CosA = 63810 - 30625
CosA = 33185/61506 = 0.54
A = Cos^(-1)0.54 = 57.32 degrees
To determine angle B, we would apply the sine rule. It states that
a/SinA = b/SinB = c/SinC.
Therefore,
175/Sin57.32 = 201/Sin B
175SinB = 201Sin57.32 = 168.84
SinB = 168.84/175 = 0.9648
B = Sin^(-1)0.9648 = 74.75 degrees
Since the sum of the angles in a triangle is 180 degrees,
C = 180 - 74.75 - 57.32 = 47.93 degrees
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<h3> The width (side perpedicular to the barn): <u>x = 8 m</u></h3><h3> The lenght (side parallel to the barn): <u>y = 16 m</u> </h3>Step-by-step explanation:
x - the width of the barn
She has 32 m of fencing so for the lenght remain (32-2x) m of fencing:
y = 32 - 2x
Area of the fencing: A = x•y
A(x) = x•(32 - 2x)
A(x) = -2x² + 32x ← quadratic function
The maximum value of quadratic function occurs at:
a = -2, b = 32
32-2x = 32 - 2•8 = 16
