Question

A triangular plot of land has one side along a straight road measuring 294 feet. a second side makes a 63degrees angle with the​ road, and the third side makes a 56degrees angle with the road. how long are the other two​ sides?

Answer 1

The side across from the 63° angle is 299.5 ft and the side across from the 56° angle is 278.7 ft.

We will use the Law of Sines to solve this.  First, the angle across from the 63° angle:
sin 61/294 = sin 63/x

Cross multiply:
x*sin 61 = 294 sin 63

Divide by sin 61:
(x sin 61)/(sin 61) = (294 sin 63)/(sin 61)
x = 299.5

For the side across from the 56° angle:
sin 61/294 = sin 56/x

Cross multiply:
x*sin 61 = 294 sin 56

Divide both sides by sin 61:
(x sin 61)/(sin 61) = (294 sin 56)/(sin 61)
x = 278.7