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Given that ∅ = 12.2° , calculate the area of the triange below
give your answer to 2 d.p.

Given that ∅ = 12.2° , calculate the area of the triange below give your answer to-example-1
User Evelise
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2 Answers

2 votes

Answer:

A = (1/4)√(4 + 11 + 14)√(-4 + 11 + 14)√(4 - 11 + 14)√(4 + 11 - 14)

A = (1/4)√29√21√7

= about 16.32 mm²

User Bschreck
by
8.2k points
4 votes

Answer:

16.27 mm² (see comment)

Explanation:

You want the area of a triangle with side lengths 11 mm and 14 mm, and the angle between them 12.2°.

Area

The area is given by the formula ...

A = 1/2ab·sin(C)

A = 1/2(11 mm)(14 mm)·sin(12.2°) ≈ 16.27 mm²

The area of the triangle is about 16.27 square millimeters.

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Additional comment

If you use Heron's formula for the area from the three side lengths, you find it is about 16.32 mm². That's the trouble with over-specified geometrical figures. The result you get depends on which of the given values you use. (To get the area accurate to 4 sf, the angle needs to be specified to 4 sf: 12.24°.)

s = (4 +11 +14)/2 = 14.5

A = √(s(s -a)(s -b)(s -c))

A = √(14.5(14.5 -4)(14.5 -11)(14.5 -14)) = √(14.5·10.5·3.5·0.5) = √266.4375

A ≈ 16.32

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Given that ∅ = 12.2° , calculate the area of the triange below give your answer to-example-1
Given that ∅ = 12.2° , calculate the area of the triange below give your answer to-example-2
User KatariaA
by
7.4k points

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