Three-Dimensional Trigonometry (Grade 12) — Worksheet & Memo

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Grade 12 · Trigonometry

Three-Dimensional Trigonometry (Grade 12)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 16

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
In the diagram below, calculate the size of DB̂C.
(2)
180° − 40° − 65° = 75°✓✓ (2)
2
In the diagram below, calculate the length of BC.
(2)
BCsin40° = 30sin75° → BC = 19,96 m✓✓ (2)
3
In the diagram below, calculate the height of the pole AB.
(2)
AB = BC tan32° = 19,96 × tan32° = 12,47 m✓✓ (2)
4
Why is AB̂C = 90° in the diagram below?
(2)
Because AB is vertical and BC lies in the horizontal plane.✓✓ (2)
5
Which triangle should you solve first in a 3-D problem?
(2)
The one with the most information — usually the horizontal triangle — so that you can find the shared side.✓✓ (2)
6
An angle of elevation is measured from which direction?
(2)
From the horizontal.✓✓ (2)
7
Calculate the area of △BCD given BC = 19,96 m, CD = 30 m and BĈD = 65°.
(2)
12(19,96)(30)sin65° = 271,40 m²✓✓ (2)
8
Can the sine rule be applied to a three-dimensional figure as a whole?
(2)
No — it applies only within a single plane triangle, so the figure must be split up.✓✓ (2)

TOTAL: 16 marks