VC2M10M03 Official strand: Measurement

Directions, elevation and depression

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Apply right-triangle methods to practical routes and measured viewing angles.

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From level ground, a person 10 m from a vertical wall measures an angle of elevation of 20° to its top. Their eye is 1.5 m above the ground. Estimate wall height to one decimal place.

A3.6 m B5.1 m C6.6 m D27.5 m

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Answer: 5.1 m

Height above eye level = 10 tan(20°).
Add the 1.5 m eye height.
The wall is approximately 5.1 m high.
tan(20°) ≈ 0.36397.
10 × 0.36397 ≈ 3.639702.
3.639702 + 3/2 ≈ 5.139702.

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Curriculum reference

Victorian Curriculum F–10 Version 2.0

Pi Leo practice scope

Apply right-triangle methods to practical routes and measured viewing angles.

Read the official VCAA curriculum description (VC2M10M03)

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VC2M10M03-C01Use a right triangle formed by horizontal distance and vertical height difference.
VC2M10M03-C02Model practical angles of elevation and depression and check assumptions.
VC2M10M03-C03Use Pythagoras for distance and trigonometry for direction.
VC2M10M03-C04Solve and communicate a practical direction or bearing problem.
VC2M10M03-C05Apply and explain directions, elevation and depression using read and connect representations.
VC2M10M03-C06Apply and explain directions, elevation and depression using calculate and explain each step.
VC2M10M03-C07Apply and explain directions, elevation and depression using build and check a model.
VC2M10M03-C08Apply and explain directions, elevation and depression using work backwards from what is known.

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Subskills

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Descriptor-derived subskills

D01
Include the observer’s heightUse a right triangle formed by horizontal distance and vertical height difference.
D02
Resolve a route into perpendicular partsUse Pythagoras for distance and trigonometry for direction.
D03
Read and connect representationsApply and explain directions, elevation and depression using read and connect representations.
D04
Calculate and explain each stepApply and explain directions, elevation and depression using calculate and explain each step.
D05
Build and check a modelApply and explain directions, elevation and depression using build and check a model.
D06
Work backwards from what is knownApply and explain directions, elevation and depression using work backwards from what is known.