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

Answer:

8.4 square units

Step-by-step explanation:

See attachment for the figure.

Trigonometric area formula is Area =$\frac{1}{2}\times absin(C)$

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 = $\frac{1}{2}\times acsin(B)$

       = $\frac{1}{2}\times acsin(B)$

       = $\frac{1}{2}\times 6\times 2\sqrt{2}\times sin(80)$

       = 6√2×sin80°

       = 6×(1.414)×0.9848

       = 8.36 square units

       ≈ 8.4 square units