Question 973279
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. 
<pre>
We draw the isosceles triangle, letting the two equal sides 
be x meters long each:

{{{drawing(2720/13,400,-17,17,-5,60,
locate(-1.8,43,"32°"),locate(-1.8,0,30m),
triangle(-15,0,15,0,0,15tan(37pi/90)),
locate(-10,26,x),locate(8.9,26,x)


  )}}}

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:

{{{drawing(2720/13,400,-17,17,-5,60,
line(0,0,0,15tan(37pi/90)),
locate(-4,36,"16°"),locate(.8,36,"16°"),
locate(-10,26,x),locate(8.9,26,x),
locate(-9,0,15m),  locate(5,0,15m),
rectangle(-2,0,0,2),
triangle(-15,0,15,0,0,15tan(37pi/90))  )}}}

Looking at either of the two congruent right triangles,

{{{sin("16°")}}}{{{""=""}}}{{{matrix(1,5,SIDE,OPPOSITE,THE,"16°",ANGLE)/HYPOTENUSE)}}}

{{{sin("16°")}}}{{{""=""}}}{{{15/x}}}

Multiply both sides by x

{{{x*sin("16°")}}}{{{""=""}}}{{{15}}}

Divide both sides by sin(16°)

{{{x}}}{{{""=""}}}{{{15/sin("16°")}}}

Use calculator:

{{{x}}}{{{""=""}}}{{{15/0.2756373558}}}

{{{x}}}{{{""=""}}}{{{54.41932918}}}

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</pre>