IGCSE Math B 9.C Elevation and depression Topic Practice

Diagram NOT accurately drawn

Figure 2 shows a vertical tower AT of height 110 m and a horizontal triangle PAQ. The base A of the tower is 600 m due north of a point P.

Calculate the size, in degrees to one decimal place, of the angle of elevation of T from P.

Diagram NOT
accurately drawn

The diagram shows two vertical masts, AB and CD, on horizontal ground.
The height of AB is 500 m and the height of CD is 350 m.
The angle of elevation of B from D is $30^{\circ}$
Calculate, to the nearest m, the distance AC.
m

In the diagram, AB represents a vertical cliff of height 65 m.
The point C, on the boat, is on the surface of the sea such that the angle of depression of C from A, the top of the cliff, is $35^{\circ}$

Calculate the distance, in m to 3 significant figures, of C from B, the bottom of the cliff.

A and B are two points on horizontal ground.
The distance from A to B is 1.5 kilometres.
BC is a vertical pole.
The angle $\angle CAB=6^\circ$.
Calculate the height, in metres to 3 significant figures, of the pole.

Diagram NOT accurately drawn.

The diagram shows quadrilateral ABCD, where B and C are on horizontal ground and BA and CD are vertical.
$$BC=12.2\text{ metres}\quad AB=1.7\text{ metres}\quad \angle ABC=\angle BCD=90^\circ$$
The angle of elevation of D from A is $32^\circ$.
Calculate the length, in metres to 3 significant figures, of CD.

A and B are two points on horizontal ground.
The distance from A to B is 20 m.
BT is a vertical pole.
The angle of depression of A from T is $10^\circ$.
Find the height, in metres to 3 significant figures, of the pole.

Diagram NOT accurately drawn.

In the diagram, AB represents a vertical wall and CD represents a vertical building.
The height of the wall is 1.4 m.
The bottom of the wall, B, and the bottom of the building, D, are on horizontal ground, such that $BD=5\text{ m}$.
The angle of elevation of C from A is $75^\circ$.
Calculate the height, in m to one decimal place, of the building.

Figure 3 shows a solid right prism ABCDEFGH.
Diagram NOT accurately drawn.
The base of the prism, ABCD, is a rectangle and is horizontal. Trapezium BCHG is a cross section of the prism.
$$AB=4\text{ m},\quad BC=3\text{ m},\quad CH=2.4\text{ m},\quad GB=1.5\text{ m}$$$$\angle GBC=\angle BCH=\angle ABG=\angle DCH=90^\circ$$

Calculate the angle of depression, in degrees to one decimal place, of G from E.