The triangle ADE shown has an area of 12 $\mathrm{cm}^2$.

a Calculate the area of triangle ABC.

b Calculate the length BC.

Two observers are 400 ft apart on opposite sides of a tree. The angles of elevation from the observers to the top of the tree are 15° and 20° .Find the height of the tree.

The angle of elevation from a ship to the top of a lighthouse is

$$4 ^ { \circ }$$

If the top of the lighthouse is known to be 50 m above sea level, how far is the ship from the lighthouse?

A woman stood on the top of a 500-ft building and measured a $20^{\circ}$ angle of elevation to an airplane flying at an altitude of 2500 ft. What was the straight-line distance from the woman to the airplane?

An airplane flying at an altitude of 9000 meters passes directly overhead. Fifteen seconds later, the angle of elevation to the plane is $60^{\circ}$. How fast is the airplane flying?

A circular ring has a cross-section as shown (left). If the outer radius is 22mm and the inner radius 20mm, calculate the cross-sectional area of the ring.

A cube and a cylinder have the same surface area. If the cube has an edge length of 6 cm and the cylinder a radius of 2 cm calculate: a) the surface area of the cube, b) the height of the cylinder.

Two buildings on opposite sides of a street are $40 \mathrm{~m}$ apart. From the top of the taller building, which is $185 \mathrm{~m}$ high, the angle of depression to the top of the shorter building is $13^{\circ}$. Find the height of the shorter building.

If the wheel of a bicysele has a diameter of 60 cm, calculate how far a cyclist will have travelled after the wheel has rotated 100 times.

The wheel of a car has an outer radius of 25 cm. Calculate: a) how far the car has travelled after one complete turn of the wheel, b) how many times the wheel turns for a journey of 1 km.

The wheel of a car has an outer radius of 25 cm. Calculate:

a how far the car has travelled after one complete turn of the wheel,

b how many times the wheel turns for a journey of 1 km.

The two packs of cheese X and Y are similar.

The total surface area of pack $Y$ is four times that of pack X. Calculate:

a the dimensions of pack $Y$

b the mass of pack $X$ if pack $Y$ has a mass of $800 \mathrm{g}$.

The rectangular floor plan of a house measures 8 cm by 6 cm. If the scale of the plan is 1 : 50, calculate:

a the dimensions of the actual floor,

b the area of the actual floor in $\mathrm{m}^2$.

Calculate the number of sides a regular polygon has if an interior angle is five times the size of an exterior angle.