Question

A bicycle race follows a triangular course. The 3 legs of the race are, in order, 2.3 km, 5.9 km, 6.2 km. Find the angle between the starting leg and the finishing leg, to the nearest degree.

How did you get the answer?

Answer 1

72°

Explanation:

when we have all the sides and need an angle, we use the law of cosine (the extended Pythagoras) :

c² = a² + b² - 2ab×cos(C)

where c is the side opposite of the angle C.

so, since the starting leg is 2.3 km, and the finishing leg is 6.2 km, we know that 5.9 km is the side opposite of the angle between the starting and finishing legs.

so, we have

5.9² = 2.3² + 6.2² - 2×2.3×6.2×cos(C)

34.81 = 5.29 + 38.44 - 28.52×cos(C)

-8.92 = -28.52×cos(C)

cos(C) = -8.92/-28.52 = 0.312762973...

C = 71.77418076...° ≈ 72°

Answer 2

About 71.77 degrees

Explanation:

The starting leg is 2.3 km and the finishing leg is 6.2 km.

Using the law of cosines C^2 = A^2 + B^2 -2AB*cos(c) where A = 2.3 km, B = 6.2 km, C = 5.9 km, and angle c is the opposite angle to side C, we get:

5.9^2 = 2.3^2 + 6.2^2 -2(2.3)(6.2)*cos(c)

cos(c) = -(5.9^2 - 2.3^2 - 6.2^2)/(2*2.3*6.2)

c = 71.77 degrees