Triangular Field and Flagpole – ++ Prep

Triangular Field and Flagpole

00:00 7 marks

A triangular field ABC has AB = 65 m, AC = 80 m and \(\angle BAC = 55^\circ\).

(a) Find the length of BC. [3]

(b) Find the area of the field ABC. [2]

A vertical flagpole, BT, is erected at point B. The angle of elevation from A to the top of the flagpole T is 15°.

(c) Find the height of the flagpole, BT. [2]

Part a

2 minutes 3 marks

Question

Find the length of BC. [3]

Hint Hint

Hint

Use the cosine rule: BC² = AB² + AC² – 2·AB·AC·cos(∠BAC).

Answer Answer
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Complete Answer

BC = 68.3 m

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Part b

2 minutes 2 marks

Question

Find the area of the field ABC. [2]

Hint Hint

Hint

Use \(\tfrac12ab\sin C\) with a = 65, b = 80, C = 55°.

Answer Answer
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Complete Answer

Area = 2130 m²

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Part c

2 minutes 2 marks

Question

Find the height of the flagpole, BT. [2]

Hint Hint

Hint

In right triangle ABT, use \(\tan15^\circ = BT/AB\).

Answer Answer
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Complete Answer

BT = 17.4 m

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