Answer:
Option B
[tex]63.4 cm^2[/tex]
Step-by-step explanation:
The area of a triangle is half the product of its base by the height.
[tex]A = 0.5bh[/tex]
Where b is the base and h is the height.
In this triangle [tex]b = 9\ cm[/tex].
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 this triangle the opposite side at the 70 ° angle is h.
Therefore we know that senx is defined as:
[tex]senx = \frac{opposite\ side}{hypotenuse}[/tex]
Where:
Opposite side = h
hypotenuse = 15 cm
x = 70°
[tex]sin(70) = \frac{h}{15}[/tex]
[tex]h = sin(70)(15)[/tex]
[tex]h = 14.09 cm[/tex]
Finally, the area is:
[tex]A = 0.5(14.09)(9)\\A = 63.4 cm ^ 2[/tex]
