Question

The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:

Answer 1

Answer:

• Angle C=15+30=45

$\\ \sf\longmapsto tan45=\dfrac{AB}{BC}$

$\\ \sf\longmapsto 1=\dfrac{AB}{14}$

$\\ \sf\longmapsto AB=14in$

Now

$\\ \sf\longmapsto tan30=\dfrac{DB}{BC}$

$\\ \sf\longmapsto \dfrac{1}{\sqrt{3}}=\dfrac{DB}{14}$

$\\ \sf\longmapsto DB=\dfrac{14}{\sqrt{3}}$

$\\ \sf\longmapsto DB=\dfrac{14}{1.732}$

$\\ \sf\longmapsto DB=8in$

Now

• AD=AB-DB=14-8=6in