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Math trigonometry non right angle help please
guys please

Math trigonometry non right angle help please guys please-example-1
User Dwardu
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1 Answer

14 votes
14 votes

Answer:

about 21.3 cm²

Explanation:

Given a triangle with three sides 6 cm, 8 cm, and 12 cm, and smallest angle 26.4°, you want the area.

Area using sine formula

A = 1/2ab·sin(C)

A = 1/2(12 cm)(8 cm)·sin(26.4°) ≈ 21.34 . . . . square units

Area using Heron's formula

The semiperimeter is ...

s = (6 +8 +12)/2 = 13

The area is ...

A = √(s(s -a)(s -b)(s -c))

A = √(13·(13 -12)(13 -8)(13 -6)) = √(13·1·5·7) = √455

A ≈ 21.33 . . . . square centimeters

The area of the triangle is about 21.3 cm².

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Additional comment

The problem with over specifying the dimensions of a geometry problem is that it is often difficult to make them consistent. Here, the area values agree to three significant figures. That is about all we can expect, given the angle precision is 3 significant figures.

Your answer depends on the set of dimensions you choose to use. It will be different yet if you use the Law of Sines to find angle A or B for the Sine Formula, especially if you round the angle value to tenths.

The attachment shows the solution using side lengths only.

Math trigonometry non right angle help please guys please-example-1
User Nuri
by
3.3k points