Find the area of the field that can be reached by the goat.

The front view of a doghouse is made up of a square with an isosceles triangle on top.

The doghouse is $1.35 \text{m}$ high and $0.9 \text{m}$ wide, and sits on a square base.

The top of the rectangular surfaces of the roof of the doghouse are to be painted.

Find the area to be painted.

Calculate the distance from Camera $2$ to the centre of the cash register.

Find $\overrightarrow{\text{AF}}$.

Find the length of the rope.

Find $\text{FÂO}$, the angle the rope makes with the platform.

Hence or otherwise, show that the volume of the reservoir is $29 600 {\text{m}}^3$.

Determine the angle of depression from Camera $1$ to the centre of the cash register. Give your answer in degrees.

Without further calculation, determine which camera has the largest angle of depression to the centre of the cash register. Justify your response.

Find the length of the rope connecting $\text{A}$ to $\text{F}$.

Find $\text{FÂO}$, the angle the rope makes with the ground.

Draw and label the angle of depression on the diagram.

Find DC.

When the ship reaches D, it changes direction and travels directly to the island at 50 km per hour. At the same time as the ship changes direction, a boat starts travelling to the island from a point B. This point B lies on (AC), between A and C, and is the closest point to the island. The ship and the boat arrive at the island at the same time. Find the speed of the boat.

Let SR = $x$. Use the cosine rule to show that $x^2-\left(76\text{cos}{43}^{\circ }\right)x+420=0$.

Find the length of EB.

Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative to the
horizontal, is 85° to the nearest degree.

Find DB.

Find Minta’s speed, in metres per hour.

Find the distance from $\text{B}$ to $\text{C}$.

Write down the size of the angle of depression from $\text{H}$ to $\text{C}$.

The following diagram shows the chord [AB] in a circle of radius 8 cm, where $\text{AB}=12\text{ cm}$.

Find the area of the shaded segment.

Find the distance from $\text{A}$ to $\text{C}$.

Find the angle of depression from $\text{M}$ to $\text{N}$.

Find $\text{CV}$.

By finding an appropriate value, determine whether Joshua is correct.

To avoid water leaking into the ground, the five interior sides of the reservoir have been painted with a watertight material.

Find the area that was painted.