Sin and Cos Rules
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Sin and Cos Rules — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionSin and Cos rules based problemsConcept Practice
2 marks~3 minCriterion A
A surveyor measures a triangular plot of land, ABCABC. Angle A=35°A = 35°, angle B=72°B = 72°, and side a=8.2a = 8.2 cm (opposite angle AA).

Calculate the length of side bb, opposite angle BB, using the sine rule:

asin⁡A=bsin⁡B\frac{a}{\sin A} = \frac{b}{\sin B}

Give your answer in centimetres, correct to 3 significant figures. [2]
Question diagram

Solutions

2QuestionSin and Cos rules based problemsAssessment Practice
2 marks~3 minCriterion D
A surveying team needs to find the straight-line distance across a river to a landmark CC on the opposite bank. Direct measurement is impossible.

The team stands at two points, AA and BB, on the same bank, measuring a baseline AB=84 mAB = 84\ \text{m}. They record the angle to the landmark from each point: ∠CAB=71°\angle CAB = 71° and ∠CBA=63°\angle CBA = 63°.

Apply the Sine Rule to find the distance ACAC, then advise the team on whether a rope of length 110 m110\ \text{m} is sufficient to reach the landmark from point AA. [2]
Question diagram

Solutions

3QuestionSin and Cos rules based problemsConcept Practice
4 marks~6 minCriterion A
Triangle ABC has sides a = 8 cm, b = 11 cm, and angle A = 35°. Study the geometric figure.
a
State the formula for the Sine Rule as applied to triangle ABC. [1 mark]
b
Calculate angle B using the Sine Rule. [1 mark]
c
Evaluate whether a second valid solution for angle B exists, justifying your answer using properties of the sine function. [2 marks]
Question diagram

Solutions

4QuestionSin and Cos rules based problemsAssessment Practice
5 marks~8 minCriterion B
A surveying team is mapping a triangular plot of land, ABCABC. Their instruments record side a=8a = 8 cm, side b=10b = 10 cm, and angle A=35°A = 35°.
a
Deduce how many distinct triangles can be formed with these conditions, showing your use of the sine rule. [2]
b
For each possible triangle, calculate angle BB and side cc. [2]
c
The surveying team must fence only the plot with the larger perimeter. Advise the team which triangle to select, justifying your answer with a comparison of both perimeters. [1]

Solutions

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