IB Mathematics Analysis and Approaches Topic SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 2

Two boats, A and B, set off from the same point $P$ at the same time. Boat A travels in a straight line at a speed of $40 km / h$ , while boat B moves in a different straight-line direction at $60 km / h$ . The angle between their paths is $6 0^{\circ}$ .

Calculate the distance between the two boats after $1.5$ hours. Give your answer to $3$ significant figures.

[4]

Question 2

SLPaper 2

A stained-glass artist is constructing a window in the shape of a square with an equilateral triangle mounted on top. The base of the triangle is the same length as the side of the square, $x$ cm, and fits perfectly along its upper edge, so this shared edge is not part of the outer boundary. The total area of the window is designed to be $500 cm^{2}$ .

State an expression for the vertical height of the equilateral triangle in terms of $x$ .

[1]

Write an expression for the area of the square in terms of $x$ .

[1]

Write an expression for the area of the triangle in terms of $x$ .

[2]

Use the total area $500 cm^{2}$ to form an equation and solve for $x$ . Give your answer to 3 significant figures.

[3]

Find the total length of the outer boundary (perimeter) of the window. Give your answer to 3 significant figures.

[1]

Question 3

SLPaper 2

In triangle $A B C$ , $A B = 8$ cm, $B C = 11$ cm, and $A \hat{B} C = 6 5^{\circ}$ .

Find the area of triangle $A B C$ .

[2]

Find the length of $A C$ .

[3]

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

[2]

Question 4

SLPaper 2

In a triangular sail, $△ A B C$ :

angle $A = 4 5^{\circ}$
angle $B = 7 5^{\circ}$
side $a = 10$ m

Calculate the length of side $b$ using the law of sines.

[3]

Find the area of the triangle.

[3]

Question 5

SLPaper 2

A hot-air balloon $P$ is anchored by two ropes to points $A$ and $B$ on level ground. The distance $A B$ is 75 m. The balloon is vertically above $P_{0}$ , and $∠ A P_{0} B = 6 0^{\circ}$ in the horizontal triangle $A B P_{0}$ .

The angles of elevation of the balloon are $2 8^{\circ}$ from $A$ and $3 7^{\circ}$ from $B$ .

Draw a fully-labelled 3-D diagram showing $A, B, P_{0}, P$ and all the given angles.

[2]

Let $A P_{0} = x$ m and $B P_{0} = y$ m. Show that $x tan 2 8^{\circ} = y tan 3 7^{\circ}$ .

[2]

Using the cosine rule in triangle $A B P_{0}$ , write an equation relating $x$ and $y$ .

[2]

Find the height $h$ of the balloon, to the nearest metre.

[2]

Now suppose instead that $P_{0}$ moves horizontally on a circle of radius $75 m$ centered at $A$ . Find the central angle (radians) and the length of the arc (metres) when the bearing of $P_{0}$ from $A$ changes from $04 5^{\circ}$ to $11 5^{\circ}$ .

[3]

If $T_{A} = k ∣ A P ∣$ and $T_{B} = k ∣ B P ∣$ , find $\frac{T _{A}}{T _{B}}$ .

[3]

IB Mathematics Analysis and Approaches SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area Questionbank

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IB Mathematics Analysis and Approaches SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area Questionbank

Unlock all 22 questions with a free account