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# Area pf a triangle ! ?

in triangle .ABC , angleA=120 , b=10 c=18 ; what's the area ?

options:

52

78

90

156

### 3 Answers

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- Anonymous9 years agoFavorite Answer
You are given two sides b and c and an included angle A, so we can use:

A = (1/2)bc*sin(A).

Therefore, the area of the triangle is:

A = (1/2)(10)(18)sin(120°) ≈ 78 square units.

I hope this helps!

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- 9 years ago
if you know the size of an angle and the values of the two adjacent sides you can use the sine formula for area

A = 1/2 ab sinC where C is the angle, and a and b are the adjacent sides

in this case

A = 1/2 * 10 * 18 *sin 120

= 90sin120

=90* √3/2

= 45√3 or 78 units squared

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- 9 years ago
You can use the law of cosines

a^2 = b^2 +c^2 - 2bc*cos(A)

a^2 = (10)^2 +(18)^2 - 2(10)(18)*cos(120)

a^2 = 604

a = 24.58

AREA = 77.94229666245037 Square Units

So the answer is 78. ;)

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