A curved section of a roadway consists of two consecutive circular arcs with radii…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

A curved section of a roadway consists of two consecutive circular arcs with radii

200\,\text{m}

and

300\,\text{m}

that meet smoothly at a common centre. The arcs subtend angles

\theta_{1}

and

\theta_{2}

(in radians) respectively, where

\theta_{2}=1.2\,\theta_{1}

. If the total length of the curved section is

280\,\text{m}

, determine the values of

\theta_{1}

and

\theta_{2}

, each correct to two decimal places.