Question

Right triangles abc and bcd with right angle c are given below. if m(a)=30∘,m(d)=45∘, and bd=12, find the length of ab. note: the triangle may not be drawn to scale.

Answer 1

Solution:

A is the right tringle ABD, C is bisects AD.

AC = CD and BD = 12

BC=BDsin(BDC)

BC=12Sin(45)

 $=12\times \frac{1}{\sqrt{2}}=\frac{12}{\sqrt{2}}$

$AB=\frac{BC}{sin(bac)}=\frac{\left | 2 \right |\sqrt{2}}{sin30}=\frac{\left | 2 \right |\sqrt{2}}{\frac{1}{2}}=\frac{12\times 2}{\sqrt{2}}$

$AB=\frac{24}{\sqrt{2}}=12\sqrt{2}$