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

From the triangle ABD:

`\begin{gathered} tan\text{ }20=(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