christmas lights question

Question

Omar is putting up Christmas lights around his triangular roof. Two of the vertices of the triangle have angles 43 ° and 37°. The side joining these vertices is 4.5 m in length. Calculate the total length of lights required to the nearest metre. Include a labelled diagram.

Answer 1

3rd angle = 180-43-37 = 100 degrees

use law of sines

sin100/4.5 = sin43/b = sin37/c

b and c are the other two sides

b = 4.5sin43/sin100 = 4.5(.682)/.985=about 3.16 meters

c = 4.5sin37/sin100 = about 2.749 meters

total length needed = perimeter = 4.5 +3.2 +2.7 = 10.4 meters = about 10 meters