DP Mathematics: Applications and Interpretation Questionbank

Find the size of $\text{AĈB}$.

Find $\text{DE}$.

Find the area of triangle $\text{DCE}$.

Estimate $\text{DF}$. You may assume the highway has a width of zero.

Given that $\sin 60°=\frac{\sqrt{3}}{2}$, show that the area of the base of the box is equal to $\frac{3\sqrt{3}{x}^2}{2}$.

Given that $\text{A}\hat{\text{B}}\text{C}$ is acute, find $\sin \theta$.

Find $\cos \left(2\times \text{C}\hat{\text{A}}\text{B}\right)$.

Calculate the length of $\text{BD}$.

Show that angle $\text{EDC}=48.0°$, correct to three significant figures.

Calculate the area of triangle $\text{BDC}$.

Pedro draws a circle, with centre at point $\text{E}$, passing through point $\text{C}$. Part of the circle is shown in the diagram.

Show that point $\text{A}$ lies outside this circle. Justify your reasoning.

Find the area of the field.

The farmer would like to divide the field into two equal parts by constructing a straight fence from $\text{A}$ to a point $\text{D}$ on $\text{[BC]}$.

Find $\text{BD}$. Fully justify any assumptions you make.

A triangular field $\text{ABC}$ is such that $\text{AB}=56 \text{m}$ and $\text{BC}=82 \text{m}$, each measured correct to the nearest metre, and the angle at $\text{B}$ is equal to $105°$, measured correct to the nearest $5°$.

Calculate the maximum possible area of the field.

A footpath is to be laid around the curved side of the lawn. Find the length of the footpath.

Find the area of the lawn.

Find the size of angle $\text{A}\hat{\text{O}}\text{B}$ in degrees.

Find the distance between points $\text{A}$ and $\text{B}$.

Find the area of the Bermuda Triangle.

Calculate the value of $\theta$, the measure of angle $\text{MŜB}$.

The following diagram shows a corner of a field bounded by two walls defined by lines $L_1$ and $L_2$. The walls meet at a point $\text{A}$, making an angle of $40°$.

Farmer Nate has $7 \text{m}$ of fencing to make a triangular enclosure for his sheep. One end of the fence is positioned at a point $\text{B}$ on $L_2$, $10 \text{m}$ from $\text{A}$. The other end of the fence will be positioned at some point $\text{C}$ on $L_1$, as shown on the diagram.

He wants the enclosure to take up as little of the current field as possible.

Find the minimum possible area of the triangular enclosure $\text{ABC}$.

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

Find $\text{CV}$.

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

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.

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

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.

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

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

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

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

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

Find the area of the shaded segment.

Find the angle $\text{AÔB}$.

Find the angle $\text{AÔB}$.

Find the area of the shaded segment.

Find CÂB.

Point B on the ground is 5 m from point E at the entrance to Ollie’s house. He is 1.8 m tall and is standing at point D, below the sensor. He walks towards point B.

Find the distance Ollie is from the entrance to his house when he first activates the sensor.

Hence find the area of triangle $\text{XYZ}$.

Find the cost per metre of installing this cable.

State why the cost for installing the cable between $\text{A}$ and $\text{F}$ would be higher than between the other buildings.

Find $\text{AF}$.

Use the cosine rule to show that $r^2-12\sqrt{3}r+144-p^2=0$.

Calculate the two corresponding values of PQ.

Hence, find the area of the smaller triangle.

Determine the range of values of $p$ for which it is possible to form two triangles.

In triangle ABC, AB = 5, BC = 14 and AC = 11.

Find all the interior angles of the triangle. Give your answers in degrees to one decimal place.

Boat A is situated 10km away from boat B, and each boat has a marine radio transmitter on board. The range of the transmitter on boat A is 7km, and the range of the transmitter on boat B is 5km. The region in which both transmitters can be detected is represented by the shaded region in the following diagram. Find the area of this region.

Show that $\text{sin}\theta =\frac{\sqrt{15}}{4}$.

Find the two possible values for the length of the third side.

Find the set of values of $k$ that satisfy the inequality .

The triangle ABC is shown in the following diagram. Given that , find the range of possible values for AB.

Find DB.

Find DC.

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.

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

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.

Use Giovanni's diagram to calculate the length of AX.

Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.

Find the percentage error on Giovanni’s diagram.

Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is formed.

Find the angle of elevation of A from D.

Calculate the area of triangle EAD.

Calculate the total volume of the barn.

Calculate the length of MN.

Calculate the length of AE.

Show that Farmer Brown is incorrect.

Calculate the total length of metal required for one support.

Find the length of EB.

Write down the angle of elevation of B from E.

Find the vertical height of B above the ground.

Write down an equation for the area of ABCDE using the above information.

Show that the equation in part (a)(i) simplifies to $3x^2+19x-414=0$.

Find the length of CD.

Show that angle $\mathrm{B}\hat{\mathrm{A}}\mathrm{E}={67.4}^{\circ }$, correct to one decimal place.

Find the length of the perimeter of ABCDE.

Calculate the length of CF.

Draw and label the angle of depression on the diagram.

Show that $\text{BD}=93\text{ m}$ correct to the nearest metre.

Calculate angle $\mathrm{B}\hat{\mathrm{C}}\mathrm{D}$.

Find the area of ABCD.

Calculate Abdallah’s estimate for the area.

Find the percentage error in Abdallah’s estimate.

the length of BD;

the size of angle DAB;

the area of triangle ABD;

the area of quadrilateral ABCD;

the length of AP;

the length of the fence, BP.

Find the size of angle $\text{C}\stackrel{\wedge }{\text{A}}\text{D}$.

Find the size of angle $\text{A}\stackrel{\wedge }{\text{C}}\text{D}$.

Find the gradient of $L_1$.

Find the coordinates of point $\text{C}$.

Find the equation of $L_2$. Give your answer in the form $ax+by+d=0$, where $a, b, d\in \mathrm{\mathbb{Z}}$.

Find the value of $k$.

Find the distance between points $\text{M}$ and $\text{N}$.

Given that the length of $\text{AM}$ is $\sqrt{45}$, find the area of triangle $\text{ANC}$.

Find the length of $\text{AD}$.

Find the size of $\text{A}\hat{\text{B}}\text{C}$.

Calculate the area of the triangular plot of land $\text{ABC}$.

Determine whether the rope can extend into the triangular plot of land, $\text{ACD}$. Justify your answer.