IB Mathematics Applications & Interpretation Topic SL…

A survey drone is monitored from a fixed launch point. Its position relative to the launch point at time $t$ seconds is given by $r=\begin{pmatrix}9\\-12\\20\end{pmatrix}+t\begin{pmatrix}0.6\\-0.8\\2.4\end{pmatrix}$ . The components represent easting (m), northing (m), and height above the launch point (m).

(a) the speed of the drone.

(b) the distance of the drone from the launch point when $t=0$ .

(e) Find the direct plan distance $AC$ and why no perpendicular construction is needed.

(f) the signal light’s height above level ground and why $OC$ , rather than $AC$ , is the adjacent side.

An assistant at landmark $A$ sights the same signal light.

(g) which observer, the one at $O$ or the assistant at $A$ , records the larger angle of elevation to the light, and the answer by comparing the two plan distances.

(e) the required follow-spot elevation angle and it from the mast’s $6^\circ$ lean.

(f) the straight sight-line distance $ET$ , whether the tilt is safe, and find the margin against the $38^\circ$ limit.

(g) the part played by the follow-spot tilt and by the sight-line distance $ET$ in the stated safety rule.

Two vertical towers, Tower $A$ and Tower $B$ , stand on horizontal ground. Tower $A$ has height $80$ m and Tower $B$ has height $50$ m. From the top of Tower $A$ , the angle of depression to the top of Tower $B$ is $12^{\circ}$ .

(a) Find the horizontal distance between the two towers.

(b) Find the direct distance from the top of Tower $A$ to the top of Tower $B$ .

Observation stations $A$ and $B$ are at the same altitude, with $B$ 5 km due east of $A$ . The ground projection plane is horizontal and contains both stations. The vertical projection $F$ of a mountain peak $T$ has bearing $030^\circ$ from $A$ and $330^\circ$ from $B$ . The angle of elevation of $T$ from $A$ is $25^\circ$ .

Give non-exact distances and times to three significant figures, bearings to the nearest $0.1^\circ$ , and other non-exact angles to three significant figures.

From observation point $O$ on level ground, two landmarks $A$ and $B$ lie in the same horizontal plane. The measured distance $OA$ is 80 m, $\angle AOB=70^\circ$ , and $\angle OAB=50^\circ$ . A signal mast base $C$ lies 30 m beyond $B$ on the straight ray from $O$ through $B$ , so $O,B,C$ occur in that order. The angle of elevation from $O$ to a light vertically above $C$ is $15^\circ$ . All angles are in degrees and all measurements are treated as exact. All sighting points are modelled at ground level.

A theatre technician stands on level ground with eye point $E$ 1.5 m vertically above ground point $G$ . The foot $F$ of a 30 m straight lighting mast is 40 m horizontally from $G$ . The mast leans $6^\circ$ from the vertical toward the technician. Its top is $T$ . The follow-spot records its tilt as the angle of elevation from the horizontal through $E$ to $T$ , and its safe limit is $38^\circ$ . No diagram is supplied; the stated cross-section contains $E,G,F,T$ .

(b) the mast’s angle to the horizontal.

(d) Find the horizontal and vertical separations from $E$ to $T$ .

(a) $AF$ , $BF$ and the position of $F$ relative to the midpoint of $AB$ .

(b) the vertical height $FT$ and the angle of elevation predicted from $B$ .

(c) An observer at $B$ reports an elevation angle of $30^\circ$ . the height this would imply and the percentage inconsistency relative to part (b).

(b) Find the plan distance $OB$ and the type of data that determines triangle $OAB$ .

(d) the plan distance $OC$ and why the 30 m is added.

(a) and a diagram showing $E,G,F,T$ , the 40 m ground distance, the 1.5 m eye height, the 30 m mast, the vertical through $F$ , and the $6^\circ$ lean toward the technician.

(c) the horizontal displacement of $T$ from $F$ and the height of $T$ above ground, using the mast’s angle to the horizontal from part (b).

IB Mathematics Applications & Interpretation SL 3.3—angles of Elevation and Depression Questionbank

IB Mathematics Applications & Interpretation SL 3.3—angles of Elevation and Depression Questionbank

IB Mathematics Applications & Interpretation SL 3.3—angles of Elevation and Depression Questionbank

IB Mathematics Applications & Interpretation SL 3.3—angles of Elevation and Depression Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 3.3—angles of Elevation and Depression Questionbank