Question

In the accompanying diagram of right trianglesABD and DBC, AB = 5, AD = 4, and CD=1. Findthe length of BC, to the nearest tenth.B54DYour answerI

Answer 1

Consider the triangle ABD.

Determine the length of side BD by using pythagoras theorem.

$\begin{gathered} (BD)^2=(AB)^2-(AD)^2 \\ BD=\sqrt[]{(5)^2-(4)^2} \\ =\sqrt[]{9} \\ =3 \end{gathered}$

Consdier the triangle BDC.

Determine the length of side BC using pythagoras theorem.

$\begin{gathered} (BC)^2=(BD)^2-(CD)^2 \\ BC=\sqrt[]{(3)^2-(1)^2} \\ =\sqrt[]{9-1} \\ =\sqrt[]{8} \\ =2.828 \\ \approx2.8 \end{gathered}$

Thus length of sdie BC is 2.8.