Solving Triangles with Given Information
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Solving Triangles with Given Information — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionWorking with Two Sides and Included Angle SASConcept Practice
2 marks~3 minCriterion A
A surveyor measures two boundary lines from a fixed corner point AA on a triangular plot of land: AB=8AB = 8 cm and AC=5AC = 5 cm on a scale drawing, with ∠BAC=60°\angle BAC = 60°.
a
State the included angle between sides ABAB and ACAC. [1]
b
The surveyor needs to confirm whether boundary BCBC is shorter than 8 cm before placing a fencing order. Using the cosine rule with cos⁡60°=0.5\cos 60° = 0.5, calculate BCBC, then advise the surveyor whether the fencing order should proceed. [1]
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Solutions

2QuestionUsing Given Side and Opposite Angle SSAAssessment Practice
2 marks~3 minCriterion B
A lifeguard sits atop a chair with a seat height of 6 m above the water. The lifeguard observes a swimmer in distress at an angle of depression of 30° from horizontal. A pier extends 8 m horizontally from the base of the chair.

Using the sine rule for the triangle formed by the chair height, the pier, and the line of sight, determine whether one or two valid triangles exist for this SSA configuration. [1]

Advise the lifeguard whether the angle of depression alone is sufficient to locate the swimmer's position along the pier, justifying your answer with reference to your result. [1]
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Solutions

3QuestionUsing Given Side and Opposite Angle SSAAssessment Practice
3 marks~5 minCriterion C
A surveyor models a triangular plot of land as triangle ABCABC, where a=7a = 7 cm, c=5c = 5 cm, and A=70°A = 70°.

The graph below shows y=sin⁡(x)y = \sin(x) for 0°≤x≤180°0° \leq x \leq 180°, with a horizontal line drawn at y=5sin⁡(70°)7≈0.671y = \dfrac{5\sin(70°)}{7} \approx 0.671.
a
Identify the two possible values of angle CC, rounding each to the nearest degree. [1]
b
Explain how the graph demonstrates that two distinct triangles are possible with the given information. [1]
c
The surveyor must choose the triangle in which angle BB is obtuse. Justify whether this condition can be satisfied with the given measurements. [1]

Solutions

4QuestionReal-Life Applications in Engineering and DesignAssessment Practice
4 marks~6 minCriterion D
A cable-stayed bridge has a vertical tower. A support cable runs from the top of the tower to a point on the deck. The cable makes an angle of elevation of 35°35° with the horizontal. The horizontal distance from the base of the tower to the point where the cable meets the deck is 4242 m.
a
Show that the height of the tower is given by h=42tan⁡(35°)h = 42\tan(35°). [1]
b
Calculate the height of the tower, giving your answer to the nearest metre. [1]
c
A safety regulation states that the cable length must not exceed 1.51.5 times the tower height. Advise the bridge engineer whether this bridge satisfies the regulation, justifying your answer with a numerical comparison. [2]
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Solutions

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