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.

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

The interior angles of regular polygons are given below. In each case calculate the number of sides the polygon has. a) $108^{\circ}$ b) $150^{\circ}$ c) $162^{\circ}$ d) $156^{\circ}$ e) $171^{\circ}$ f) $179^{\circ}$

For a place north of the Arctic Circle, such as Prudhoe Bay, Alaska $\left(70^{\circ} \mathrm{N}\right)$. the formula gives a negative value for the angle of elevation of the sun at noon at the winter solstice. What does this mean?

Simplify.

$$7 \sqrt{63}$$

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

a Calculate the area of triangle ABC.

b Calculate the length BC.

A cuboid has dimensions as shown in the earlier diagram : If the cuboid is enlarged by a scale factor of 2.5, calculate:
a) the total surface area of the original cuboid b) the total surface area of the enlarged cuboid c) the volume of the original cuboid d) the volume of the enlarged cuboid.

The diagram dicussed before shows a scale model of a garage. Its width is 5cm, its length 10 cm and the height of its walls 6cm.
a) If the width of the real garage is $4 \mathrm{~m}$, calculate: i) the length of the real garage ii) the real height of the garage wall.b) If the apex of the roof of the real garage is $2 \mathrm{~m}$ above the top of the walls, use Pythagoras' theorem to find the real slant length $l$. c) What is the area of the roof section A on the model?

Define wat, batik, longhouse.

An equilateral triangle has an area of $25 \ cm^{2}$. If the lengths of its sides are reduced by 15%, calculate the area of the reduced triangle.

Simplify.

$$4 \sqrt{28}$$

Consider a trapezium ABCD with AB=CD and BC parallel to AD. Given that AB = 12 cm, BC = 13 cm, and CD = 22 cm,

a. show that the trapezium has height 12 centimetres.

b. Hence, find the area of the trapezium.

c. Find the size of the angle C.

d. Calculate the length of the diagonal AC.

In the trapezium calculate the lengths of the sides e and f.

Complete the statement.

If $\sin B=\frac{8}{17}$, then $\cos B=\underline{\text { ? }}$.