Mathematics

Problem

A ladder

10\text{ m}

long rests against a vertical wall and makes an acute angle

\theta

with the horizontal ground. For this position it is known that

\cos\theta=\dfrac{4}{5}

. a. (i) Find the value of

\sec\theta

. b. (ii) Calculate how high up the wall the ladder reaches. c. (iii) If the ladder is moved so that the new angle

\theta'

satisfies

\sin\theta'=\sin\theta

, state, with reason, whether

\sec\theta'

will be equal to, greater than or less than the value obtained in part (i).