Paper 2 Section C Practice

Solution of Triangles • 10-Mark Mastery

SPM Paper 2 Section C Specialty

Form 4 Chapter 9: Solution of Triangles (Penyelesaian Segi Tiga)

Total Marks: 40 Marks • Time Allowed: 50 Minutes

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A Bahagian A: Ambiguous Case & Fundamentals [10 Marks]

Answer all questions
Soalan 1 [6 Marks]

In $\triangle PQR$, $PQ = 14\text{ cm}$, $QR = 9\text{ cm}$, and $\angle QPR = 32^\circ$.

(a) Prove that an ambiguous case exists for $\triangle PQR$. [2 marks]

(b) Calculate the two possible values of $\angle PRQ$. [2 marks]

(c) Sketch the two possible triangles $PQR_1$ and $PQR_2$ on the same diagram. [2 marks]

Soalan 2 [4 Marks]

A triangular metal plate has side lengths $a = 13\text{ cm}$, $b = 14\text{ cm}$, and $c = 15\text{ cm}$. Using Heron's formula, calculate the area of the metal plate, and deduce the radius $r$ of the inscribed circular pipe if $\text{Area} = r \times s$.

B Bahagian B: SPM Paper 2 Section C Full Blueprint [20 Marks]

Answer both 10-mark questions
Soalan 3 (Paper 2 Section C Model) [10 Marks]

Diagram below shows a quadrilateral $PQRS$ representing a solar farm layout.

P Q R S PQ = 60 m QR = 85 m SR = 70 m PS = 90 m $\angle PQR = 110^\circ$

It is given that $PQ = 60\text{ m}$, $QR = 85\text{ m}$, $PS = 90\text{ m}$, $SR = 70\text{ m}$, and $\angle PQR = 110^\circ$.

(a) Calculate the length, in $\text{m}$, of the diagonal $PR$. [3 marks]

(b) Calculate $\angle PSR$. [3 marks]

(c) Calculate the total area, in $\text{m}^2$, of the solar farm $PQRS$. [2 marks]

(d) A point $T$ lies on the line $PR$ such that the distance from $Q$ to $T$ is the shortest. Calculate the distance $QT$. [2 marks]

Soalan 4 (3D Spatial Section C Model) [10 Marks]
A telecommunications mast $VE$ of height $h$ meters stands vertically at point $E$ on a horizontal triangular foundation $ABC$. It is given that on the ground: $AB = 25\text{ m}$, $BC = 32\text{ m}$, and $AC = 40\text{ m}$. The foot of the mast $E$ is positioned on the edge $AC$ such that $AE:EC = 3:5$.

(a) Calculate $\angle BAC$ of the triangular foundation. [3 marks]

(b) Calculate the distance $BE$ on the ground. [3 marks]

(c) Given that the angle of elevation of the top of the mast $V$ from point $B$ is $28^\circ$, calculate the vertical height $VE$ of the mast. [2 marks]

(d) Hence, calculate the angle of depression of point $C$ from the top of the mast $V$. [2 marks]