DP Mathematics: Analysis and Approaches Questionbank

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

Find the length of new fence required.

Find the length of each blade of the windmill.

Given that point $\text{A}$ is $12$ metres from the base of the windmill, find the height of point $\text{C}$ above the ground.

Find the angle of elevation of point $\text{C}$ from point $\text{B}$.

Find the three-figure bearing on which airplane $B$ is travelling.

Find the distance from the camp to point C.

Find the distance from point A to point B.

Show that $\text{A}\stackrel{\wedge }{\text{B}}\text{C}$ is 101°.

Find the bearing that Jacob must take to point C.

Jacob hikes at an average speed of 3.9 km/h.

Find, to the nearest minute, the time it takes for Jacob to reach point C.

Find $\text{B}\stackrel{\wedge }{\text{C}}\text{A}$.

Show that $\text{AC}=7\text{ cm}$.

The shape in the following diagram is formed by adding a semicircle with diameter [AC] to the triangle.

Find the exact perimeter of this shape.

The following diagram shows triangle PQR.

Find PR.

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

Hence or otherwise, find the total distance along the road where the signal from the tower can reach cellular phones.

Find BD.

The area of triangle ABD is 18.5 cm². Find the possible values of θ.

Barry is at the top of a cliff, standing 80 m above sea level, and observes two yachts in the sea.
“Seaview” $(S)$ is at an angle of depression of 25°.
“Nauti Buoy” $(N)$ is at an angle of depression of 35°.
The following three dimensional diagram shows Barry and the two yachts at S and N.
X lies at the foot of the cliff and angle $\text{SXN}=$ 70°.

Find, to 3 significant figures, the distance between the two yachts.

Calculate the angle of depression from A to B.

A vertical pole, TB, is constructed at point B and has height 25 m.

Calculate the angle of elevation of T from, M, the midpoint of the side AC.

Draw and label the angle of depression on the diagram.

Find the angle of elevation from B to C.

Write down the angle of elevation of B from E.

Calculate CD, the height of the observation deck above the ground.

On the diagram, draw and label with an x the angle of depression of B from P.