Question

Tom, Aaron, and Harry are camping in their tents. If the distance between Tom and Aaron is 153 feet, the distance between Tom and Harry is 201 feet, and the distance between Aaron and Harry is 175 feet, what is the angle between Aaron, Harry, and Tom?

Answer 1

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