Question

In △ABC, AB=9.2 ft, BC=11.9 ft, and m∠B=27°.

What is the area of △ABC?



Enter your answer as a decimal in the box.
Round only your final answer to the nearest hundredth.
thanks

Answer 1

To calculate the area of a triangle you need the base & the altitude to this base:

Area triangle = 1/2(B x H)

Let's draw the altitude A intersecting BC in H. WE get now a right triangle AHB. We know AG = 9.2 we know the angle B =27°, so we can find the altitude AH through trigonometry :
sin(B) = opposite side over hypotenuse
sin(27°) = AH/AB==> sin(27°) =0.454 ==0.454= AH/9.2==>AH =0.454*9.2

AH = 4.177

Area triangle ABC = (1/2) * 11.9 * 4.177= 24.85