IB Mathematics Analysis and Approaches SL 3.3—angles of Elevation and Depression, Bearings Questionbank

Find the length of the ladder required to reach the top of the building.

The angle between the ladder and the horizontal surface it stands on should be between $70^{\circ}$ and $80^{\circ}$. Determine whether the ladder in this situation is safe.

The fire truck is moved to a horizontal distance from the building that makes the angle $72^{\circ}$. Find the length that the ladder now has to be extended to.

Making the figure according to the question. [M1][A1]

Here $\mathrm{AB}=5$ and let $\mathrm{BD}=\mathrm{CD}=h$, to find.

Also $\angle \mathrm{CAD}=90^{\circ}-60^{\circ}=30^{\circ}, \angle \mathrm{CBD}=45^{\circ}, \angle \mathrm{DCA}=60^{\circ} \quad[\mathrm{A} 1]$ Using the sine rule, $\frac{\sin 60^{\circ}}{5+h}=\frac{\sin 30^{\circ}}{h} \quad$ [M1][A1] $\frac{\sqrt{3}}{2(5+h)}=\frac{1}{2 h}$ [M1] $\sqrt{3} h=5+h$ [M1][A1] $0.732 h=5$ [M1] $h=\frac{5}{0.732} \approx 6.83 \mathrm{~m}$ [A1]