Question

Find the length of BC to the nearest whole number.

Answer 1

For the given figure, we will find the length of BC

From the triangle ABC:

$\begin{gathered} tan\text{ }65=\frac{AB}{BC} \\ \\ so,AB=BC*tan\text{ }65\rightarrow\left(1\right) \end{gathered}$

From the triangle ABD:

$\begin{gathered} tan\text{ }20=\frac{AB}{BD} \\ so,AB=BD*tan\text{ }20\rightarrow\left(2\right) \end{gathered}$

From (1) and (2)

$BC*tan\text{ }65=BD*tan\text{ }20$

note, as shown BD = 15 + BC

So,

$BC*tan\text{ }65=\left(15+BC\right)*tan\text{ }20$

Solve the equation to find BC

$\begin{gathered} BC*tan\text{ }65=15\text{ }tan\text{ }20+BC*tan\text{ }20 \\ BC\left(tan\text{ }65+tan\text{ }20\right)=15\text{ }tan\text{ }20 \\ \\ BC=\frac{15\text{ }tan\text{ }20}{(tan\text{ 6}5+tan\text{ }20)}=2.176 \end{gathered}$

Rounding to the nearest whole number

So, the answer will be BC = 2