A bicycle race follows a triangular course. The three legs of the race are, in order; 2.3km, 5.9km, and 6.2km. Find the angle between the starting line and the finishing line.
The answer I got is 18.23 degrees. Is it correct?
Puzzling
Nope, 71.774°
Wayne DeguMan
The 'cosine rule' states:
a² = b² + c² - 2bcCosA
Now, the angle is between the 2.3 and 6.2 lines, hence the side opposite is the 5.9.
i.e. a = 5.9, b = 2.3 and c = 6.2
so, 5.9² = 2.3² + 6.2² - 2(2.3)(6.2)CosA
=> CosA = (2.3² + 6.2² - 5.9²)/[2(2.3)(6.2)]
i.e. CosA = 8.92/28.52
so, A = Cos⁻¹(8.92/28.52) => 71.8°...to 3 s.f.
:)>
Elizabeth M
No, it is 180 -71.77 =108.23 degrees.