Answer:
Option A
10.5 m²
Step-by-step explanation:
The area of a triangle is half the product of its base by its height.
[tex]A = 0.5bh[/tex]
Where b is the base and h is the height.
In this triangle b = 6.1 m.
The height of this triangle is a line perpendicular to its base that goes to the vertex opposite the base.
We do not know this length. But this line h divides the triangle into two rectangular triangles.
So for these two triangles the angle that is opposite to the height h is: 47 °
Therefore we know that senx is defined as:
[tex]senx =\frac{opposite side}{hypotenuse}[/tex]
Where:
Opposite side = h
hypotenuse = 4.7 m
x = 47
[tex]Sin(47) = \frac{h}{4.7}\\\\h = (sin47)(4.7)\\\\h = 3.437[/tex]
Finally, the area is:
[tex]A = 0.5(3.437)(6.1)\\\\A = 10.5m^2[/tex]
