18N.2.SL.TZ0.S_7

pestleMathematicsAISLPaper 218N· sl-3-2-2d-and-3d-trigsource ↗

A communication tower, T, produces a signal that can reach cellular phones within a radius of 32 km. A straight road passes through the area covered by the tower’s signal.

The following diagram shows a line representing the road and a circle representing the area covered by the tower’s signal. Point R is on the circumference of the circle and points S and R are on the road. Point S is 38 km from the tower and RŜT = 43˚.

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

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

recognizing TR =32 (seen anywhere, including diagram) A1

correct working A1

eg ${32^2} = {x^2} + {38^2} - 2\left( x \right)\left( {38} \right){\text{cos}}\,43^\circ$ , $1024 = 1444 + {x^2} - 76\,\left( x \right){\text{cos}}\,43^\circ$

${x^2} - \left( {76\,{\text{cos}}\,43^\circ } \right)x + 420 = 0$ AG N0

[2 marks]

Examiners’ report

[N/A]