Question

Triangle A B C is shown. The length of B C is 6 and the length of A B is 2 StartRoot 2 EndRoot. Angle A B C is 80 degrees. Trigonometric area formula: Area = One-half a b sine (C) What is the area of ΔABC? Round to the nearest tenth of a square unit. 3.9 square units 8.4 square units 11.8 square units 17.7 square units

Answer 1

8.4 square units

Explanation:

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Answer 2

8.4 square units

Explanation:

See attachment for the figure.

Trigonometric area formula is Area =
`(1)/(2)* absin(C)`

Where a and b are two sides of the triangle and C is the angle between these two sides.

Given:

side a = 6 units, c = 2√2 units and ∠B = 80°

Then area of the triangle :

Area =
`(1)/(2)* acsin(B)`

=
`(1)/(2)* acsin(B)`

=
`(1)/(2)* 6* 2√(2)* sin(80)`

= 6√2×sin80°

= 6×(1.414)×0.9848

= 8.36 square units

≈ 8.4 square units