Law of cosines and sines

Question

a corner of Theodore wirth park occupies a triangular area that faces two streets that meet at an angle measuring 85. 

The sides of the area against the streets are 60ft and 70ft, respectively. If the landscaper wants to place tulips around the triangular area what is the peimeter he will have to work with? 

Answer 1

What you want to find is the length of the third side. Since you already have two sides and the angle between them, you use the law of cosines:

 

c² = a² + b² -2ab cos C

 

In this case, a = 60, b = 70, and C = 85°.  And c is the side you are trying to find.

 

c² = 60² + 70² - 2*60*70 cos 85°

= 3600 + 4900 - 8400 * cos 85°

= 8500 - 732.1 = 7767.9

 

So c = √7767.9 = 88.1

 

Therefore the three sides are 60, 70 and 88.1, for a total perimeter of 218.1 feet.