Circles, SM-Bank 053

Town A is 135\(^\circ\) east of Town B along the equator, as shown on the diagram below.

Given the earths' radius is approximately 6400 kilometres, calculate the distance \(d\), between the two towns. Give your answer correct to the nearest whole kilometre. (2 marks)

NOTE: \(\text{Arc length}=\dfrac{\theta}{360}\times 2\pi r\)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

\(15\ 080\ \text{km (nearest whole kilometre)}\)

Show Worked Solution

\(d\)	\(=\dfrac{\theta}{360}\times 2\pi r\)
	\(=\dfrac{135}{360}\times 2\pi \times 6400\)
	\(=15\ 079.6447\dots\)
	\(=15\ 080\ \text{km (nearest whole kilometre)}\)

\(\therefore\ \text{Towns A and B are }15\ 080\ \text{kilometres apart.}\)