Pearson Edexcel IAL Mathematics P1.3.1 Sine rule, cosine rule & triangle area

Practise applying sine rule, cosine rule and triangle area formulae to find angles, side lengths and areas from geometric diagrams.

Exam points

use the cosine rule to find an angle or side when two sides and the included angle are involved
apply 1/2ab sin C to connect a triangle area with unknown side lengths or angles
handle ambiguous sine rule cases by selecting the angle consistent with the diagram

[Maximum number: 3]

Figure 1

Figure 1 shows the plan view for the design of a stage.
The design consists of a sector OBC of a circle, with centre O, joined to two congruent triangles OAB and ODC.

Given that
- angle B O C=2.4 radians
- area of sector $B O C=40 \mathrm{~m}^{2}$
- AOD is a straight line of length 12.5 m

the total area of the stage, giving your answer, in $\mathrm{m}^{2}$ , to one decimal place,

$\frac{1}{2}\times 5.77\times 6.25\times \sin(0.37)=6.5377\ldots$

M1

Area of stage $=40+2\times\frac{1}{2}\times5.77\times6.25\times\sin(0.37)$

dM1

$=53.1\text{ m}^2$

A1

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P1.3.1 - Sine rule, cosine rule and triangle area question 1