Janver, Karl, and Adrian are camping in their tents forming a triangle. If the distance between Janver and Karl is 153 ft., the distance between Janver and Adrian is 201 ft., and the distance between Karl and Adrian is 175 ft., what is the measure of the angles formed in the triangle?
Janver is point A, Karl is point B, and Adrian is point C. I included an illustration to make this a little less confusing (it’s not to scale though).
Karl and Adrian = a = 175 ft.
Adrian and Janver = b = 201 ft.
Janver and Karl = c = 153 ft.
⁻¹
To find the angles, we can use the cosine law formula. The actual computation for the angle is done via a calculator function which I do not know how to do manually (nor were we taught how to).
[tex]cos A = \frac{b^{2} + c^{2} – a^{2}}{2bc}[/tex]
cos A = [(205ft)² + (153ft)² – (175ft)²]/2(201ft)(153ft)
cos A = 34809ft²/61506ft²
cos A = 0.565944785…
cos⁻¹ A = 55.53˚
[tex]cos B = \frac{a^{2} + c^{2} – b^{2}}{2ac}[/tex]
cos B = [(175ft)² + (153ft)² – (205ft)²]/2(175ft)(153ft)
cos B = 12009ft²/53550ft²
cos B = 0.224257703…
cos⁻¹ B = 77.04˚
For the last angle, we can simply add the first two and then subtract it from 180˚.
C = 180˚ – (A + B)
C = 180˚ – (55.53˚ + 77.04˚)
C = 180˚ – 132.57˚
C = 47.43˚
If you check with online calculators, there may be a small margin of error, but these answers are generally correct.
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