SOLUTION: The length of the base of an isosceles triangle is 30m. The angle opposite the base measures 32° find the perimeter of the triangle to the nearest metre.

We draw the isosceles triangle, letting the two equal sides 
be x meters long each:



Now we draw an altitude, which is also a median, a perpendicular bisector
of the base and the bisector of the vertex angle, which cuts the triangle 
into two congruent right triangles.
Therefore the 32° angle is cut into two 16° angles and the 30m base is cut 
into two 15m segments:



Looking at either of the two congruent right triangles,





Multiply both sides by x



Divide both sides by sin(16°)



Use calculator:





So the 3 sides of the triangle are

30m, 54.41932918m, 54.41932918m

So the perimeter is the sum of the three sides,
or

perimeter = 138.83865836m

To the nearest meter is 139m

Edwin