A course in the shape of a triangle consists of a running path, biking path, and skateboarding

path. The biking path is 51 meters long and the skateboarding path is 64 meters long. If the

angle between the running and biking paths is 78", find the angle between the running and

skatebording paths to the nearest tenth of a degree.

The angle the running and the skateboarding path ≈ 51.2° (to the nearest tenth)

Step-by-step explanation:

The course takes the shape of a triangle. That means it has three sides.

One side of the triangle (biking path) = 51 meters, another side (skateboarding) = 64 meters. The angle opposite the skateboarding path = 78°. The angle opposite the biking path is what we are ask to find.

Using sine rue we can find the angle opposite the biking path which is the angle between the running and skateboarding path. Note we used the sine rule because 2 sides are given and a non included angle

a/sin A = b/sin B = c/sin C

51/sin A = 64/sin 78°

cross multiply

51 sin 78° = 64 sin A

sin A = 51 sin 78°/64

sin A = (51 * 0.97814760073) / 64

sin A = 49.8855276374/64

sin A = 0.77946136933

A = sin⁻¹ 0.77946136933

A = 51.2112853091

A ≈ 51.2° (to the nearest tenth)