Some Applications of Trigonometry question bank (Maths)

An electrician has to repair an electric fault on a pole of height $5\, m$. She needs to reach a point $1.3\, m$ below the top of the pole to undertake the repair work (see figure). What should be the length of the ladder that she should use which,when inclined at an angle of $60^{\circ}$ to the horizontal,would enable her to reach the required position? Also,how far from the foot of the pole should she place the foot of the ladder? (You may take $\sqrt{3}=1.73$)

An observer $1.5\, m$ tall is $28.5\, m$ away from a chimney. The angle of elevation of the top of the chimney from her eyes is $45^{\circ}$. What is the height of the chimney? (in $m$)