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The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:
What is the length of the wood that is needed to replace AD?

The figure below shows a triangular wooden frame ABC The side AD of the frame has rotted and needs to be replaced What is the length of the wood that is needed class=

Respuesta :

Answer:

  • Angle C=15+30=45

[tex]\\ \sf\longmapsto tan45=\dfrac{AB}{BC}[/tex]

[tex]\\ \sf\longmapsto 1=\dfrac{AB}{14}[/tex]

[tex]\\ \sf\longmapsto AB=14in[/tex]

Now

[tex]\\ \sf\longmapsto tan30=\dfrac{DB}{BC}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{\sqrt{3}}=\dfrac{DB}{14}[/tex]

[tex]\\ \sf\longmapsto DB=\dfrac{14}{\sqrt{3}}[/tex]

[tex]\\ \sf\longmapsto DB=\dfrac{14}{1.732}[/tex]

[tex]\\ \sf\longmapsto DB=8in[/tex]

Now

  • AD=AB-DB=14-8=6in

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