Answer:
[tex]\large\boxed{A=89.6}[/tex]
Step-by-step explanation:
It's the right triangle. The formula of an area of a right triangle:
[tex]A=\dfrac{leg\cdit leg}{2}[/tex]
We have:
[tex]leg=x\\leg=16\\\text{and the angle}\ \alpha=55^o[/tex]
Use tangent:
[tex]tangent=\dfrac{opposite}{adjacent}[/tex]
[tex]opposite=16,\ adjacent=x[/tex]
[tex]\tan55^o\approx1.4281[/tex]
Substitute:
[tex]\dfrac{16}{x}=1.4281[/tex] convert the decimal to the fraction
[tex]\dfrac{16}{x}=\dfrac{14281}{10000}[/tex] cross multiply
[tex]14281x=160000[/tex] divide both sides by 14281
[tex]x=\dfrac{160000}{14281}[/tex]
[tex]x\approx11.2[/tex]
Calculate the area:
[tex]A=\dfrac{(16)(11.2)}{2}=89.6[/tex]
