construct a triangle has a perimeter 110mm and the base angles are 48degrees and 70 degrees

Question

a triangle ABC has a perimeter of 110mm and base angles are 48degree and 70 degree.construct this triangle with the information given

Answer 1

The third angle of the triangle is 180-(70+48)=62 degrees.

We can use the sine rule:

a/sin70=b/sin48=(110-(a+b))/sin62 because we know the perimeter is 110mm.

From this a/sin70=(110-(a+b))/sin62.

Cross-multiply: asin62=(110-(a+b))sin70=110sin70-asin70-bsin70.

a(sin62+sin70)=(110-b)sin70; a=(110-b)sin70/(sin62+sin70).

But a=bsin70/sin48, therefore bsin70/sin48=(110-b)sin70/(sin62+sin70).

Therefore: b/sin48=(110-b)/(sin62+sin70).

Cross-multiply: bsin62+bsin70=110sin48-bsin48, b(sin62+sin70+sin48)=110sin48.

Therefore b=110sin48/(sin62+sin70+sin48)=31.86mm approx.

Since a=bsin70/sin48, a=110sin70/(sin62+sin70+sin48)=40.29mm approx and the third side=37.85mm.

The third side is the base and the angles at each end of the base can be constructed to form the other two sides.